Is "princessship" a real word? Are there any other words which have the same letter 3 times consecutively?

Solution 1:

There is no word with three consecutive letters under the most narrow definition of "real word", but there are several words of the following types:

1. There are many acronyms/initialisms that contain triple letters, like AAA, AIEEE, KKK, WWW, or Roman numerals like xviii.

2. There are place names, like

   • Kaaawa, a place in Hawaii.
   • Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch, a place in Wales.

3. There are names of people with all sorts of unconventional spellings, like Minnnie, Annnora, or Diannne.

4. There are interjections like mmm, hmmm, zzz, etc.

5. There are archaic/poetic words with elided letters, like whenceeer (really, whencee'er from whenceever), wheree'er, etc.

6. Finally, there are words which would probably be written with a hyphen whenever used, like frillless (mentioned by Dusty) which is really frill-less, similarly bulllike, gulllike, wallless, many words ending in -ss-ship like your princessship, bossship, goddessship, headmistressship, patronessship.

Solution 2:

I'm not a native speaker, but I'm under the impression that words with the same letter repeated three times are either elided so that they contain two, or are spelled with a hyphen.

For instance cross-section (hyphenated) or chaffinch (where the 3rd 'f' is omitted)

Solution 3:

I believe princessship is typically spelled with a hyphen princess-ship, although I do remember references to it without. However, if your friend is willing to allow princessship as a word, certainly words like dutchessship, governessship, countessship, etc. would also qualify.

So one way or another, you can prove your friend wrong =D

Edit: A quick search also brings up frillless which has an entry in OED