Why does "one half" have no hyphen, but "two-thirds" does?

The Chicago Manual of Style has these guidelines:

For compounds formed with fractions:

• The noun form is open (a half hour)
• The adjective form is hyphenated (a half-hour session)

For simple fractions:

• Hyphenated in noun, adjective, and adverb forms, except when second element is already hyphenated (one-half; one and three-quarters; one twenty-fifth)

So "1/2" should always be written out as one-half. (Unless it's in a sentence like "one half of a perfect pair," in which case it's not a fraction.)

One half need not be hyphenated when used as a noun; however, it must be hyphenated when used as an adjective:

 1. I am entitled to one half of the pizza.
 2. I have a one-half interest in the pizza.

It is correct to have the hyphen. I am not quite sure why the people that you see write "one half" do not write "one-half" but they should!

Searching for "one half" at dictionary.reference.com does not return any results, but searching for "one-half" does.

One-half dictionary.reference.com

This is the same for "two-thirds".

Two-thirds dictionary.reference.com