What is the source of "Long time no see," and when did it enter U.S. English?

1. Did "long time no see" arrive in U.S. English from forms of pidgin English spoken separately by both some Native Americans and some Chinese immigrants?

The earliest recorded examples are from native Americans, but it's plausible it was used in other types of pidgin English at the same time.

2. When did this turn of phrase first gain the recorded notice of an American English-speaking author?

It has been recorded by American English-speaking writers in 1900. The author Raymond Chandler used it in a 1939 newspaper and 1940 book.

3. When did the phrase cross over into use by native U.S. English speakers among themselves?

Chandler presumably helped popularise it with detective stories and film noir of the early forties.

The OED says it's a "Colloq. phr. (orig. U.S.) long time no see, a joc. imitation of broken English, used as a greeting after prolonged separation."

Their earliest quotation is 1900 from a native American:

1900 W. F. Drannan Thirty-one Years on Plains (1901) xxxvii. 515 When we rode up to him [sc. an American Indian] he said: ‘Good mornin. Long time no see you.’

Their next quotation of 1939 shows it was fully naturalised:

1939 R. Chandler in Sat. Evening Post 14 Oct. 72/4 Hi, Tony. Long time no see.

Their next is also from Chandler, in 1940's Farewell, my Lovely.

It's interesting to note that by 1880, 10% of California's inhabitants were Chinese ("Made in America" by Bill Bryson, p. 143.) Such a high influx of Chinese were flooding in that America passed the Chinese Exclusion Act of 1882 to specifically prohibit more Chinese from immigrating.

In light of that, and Sven Yargs quote above from the article "Lee Hing's Girl," in the Seattle Post-Intelligencer (February 14, 1892, predating the OED quotation), it seems that a strong case can be made for attributing the popularity of "Long Time No See" in the American West to a Chinese origin rather than a Native American. It is, after all, a very popular greeting in Chinese (I lived in China from 2003-2011), and apparently was in use in Chinese at that time (according to D. Robb's comment above). It is also a greeting that uses those four words exactly.

This might be a rare OED mistake.

I found one somewhat earlier instance—from early 1892—in a newspaper archived in the Library of Congress's Chronicling America database of old newspapers. From "Lee Hing's Girl," in the Seattle Post-Intelligencer (February 14, 1892), attributed to the New York Sun but with no date for the occurrence in that newspaper (which further searches in the database did not disclose):

"Good by, Mamie," said Sing, as he unbolted the door for the girl. "You come back tonight?"

"Maybe. I think I go see my mamma today. Long time no see," answered Mamie, who from constant association, had, like the other girls of the neighborhood, fallen into the habit of talking pigeon English to the Chinamen. "Good by."

The phrase is repeated multiple times a bit later in this surprisingly racy (and, not surprisingly, racist) story, always in the context of its being pidgin English spoken in a Chinese-American milieu.

There may well be other instances of the phrase in the Library of Congress database, but checking all of the supposed matches for "long time no see" is a daunting task: Even when you bundle the phrase in quotation marks, the search tool returns matches for all pages that include the four words long, time, no, and see, which translates into 2405 matches for the years 1836–1900, many of which actually contain phrases such as "long time to see" or "long time not seeing."

UPDATE (December 5, 2016):

An Elephind search yields three even earlier matches for "long time me no see"—two of which involve a Chinese speaker and the other a Native American speaker. First, from the Marysville [California] Daily Appeal (May 7, 1874):

HONORABLE CHINAMAN.—Tuck Wah, butcher on the corner of First street and Maiden Lane, appears to be a very honorable person for a "heathen Chinee." John [presumably, Tuck Wah] lost about thirty hogs some time ago, and concluded they had gone from his gaze forever. P. C. Slattery a week ago advertised a lot of swine as occupying his fields, and notified the owner to call, pay charges and take them away. The hogs proved to belong to Tuck Wah, and he called on Mr. Slattery for them, saying: "You good man; I good man; how muchee me, pay you keep hogge? Me tinkee durty dollar rightee." Mr. Slattery was a little surprised at the honorable offer of Tuck Wah, and told him that $10 would pay all the damages. The Chinaman felt that he had been outdone in magnanimity. They are so generally robbed when in the power of white men that no wonder he was surprised. He therefore broke out into another long lingo of laudation, in American-Chinese dialect, something like the following: "Me goode man; you goode man; me tinkee you belly good man; mo no sabe mucha man ebry day; long time me no see 'Melikan man no taka durty dollar for ten dollar."

Next from "A Jaunt Down the Colorado," in the [Yuma] Arizona Sentinel (February 20, 1886):

Homeward bound wood was taken on, and head Chief Hockorow, of the Cocopah Nation, his dark face beaming with pleasure, saluted our commander with "How! Polhamus, long time me no see, no catch 'um boat comida heap long," which statesmanlike and diplomatic salute was duly recognized with a bounteous repast at the galley mess, and the distended abdominal recess of the Chieftian gave ample evidence of his labor of love.

And finally from "Hop Sing Writes to the Champion," originally in the Downey [California] Champion, reprinted in the Los Angeles [California] Herald (July 17, 1890):

When he [a Chinese immigrant in the United States] go to get some papers so he be all same as Mellican man and heap vote you no let him have any. So what he do, he send him money home to China and bymeby he go to. Now Mellican man when he got to China he no work, he ketchum heap fine coat heap long hat and heap nice cane, and pleach, pleach all the time, he tell all Chlistians here good, Confucius no good. Now me live in China long time me no see heap dlunk Chinaman, me come to California me every day see heap dlunk Chlistains. Saloon man he gitum lots money.

The four earliest instances of the phrase that I'm aware of come from three far western states of the United States—California (two occurrences) Arizona, and Washington—and this fact raises the possibility that native English speakers there may have built their own notion of a kind of universal pidgin English to serve as a lingua franca and attributed it indiscriminately to both Native Americans and immigrant Chinese.

Clearly the American reporters see some special features of Chinese pidgin English (a tendency to to add -ee endings to simple English words and of course l-for-r confusion) from Native American pidgin English; but in other respects—including "long time me no see," use of heap as a generic intensifier, and use of "catch 'um"/"ketchum" for obtain—the attributed word choices are strikingly similar, especially as between the 1896 Yuma, Arizona, item involving a Native American speaker and the 1890 Downey, California, item involving an immigrant Chinese speaker.

In other words, the earliest uses of the phrase suggest three possible sources of "long time no see" as an idiomatic English phrase: Chinese speakers trying to communicate with native English speakers in English; Native American speakers trying to communicate with native English speakers in English; and native English speakers of the western United States trying to communicate with members of those two groups "in a language they can understand."

My grandfather spent from 1895 to 1922 in South China. He had several Pidgin English expressions that slipped into his conversation, one of which was "long time no see." Another was "What for no like?", the meaning obvious. Another rather common one was to hurry, "You go chop-chop."