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Know Your Phrase - The Meanings For Common Phrases and Idioms > T-Letter Sayings
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Phrases and Idioms
knowyourphrase.com - The Meanings and Origins For Several Common Idioms and Phrases
T
High quality, exceptional; something that's very valuable.
This phrase is said to have derived from the British expression 'out of the top drawer,'
which used to be a way to describe someone's social status. The drawers refer to
chests that have several drawers from top to bottom, and usually the more valuable
things are kept at the top for easier access.

This saying looks to have been made popular around the early 1900s. An example
of that is seen in The Argus, October 1926, where it reads:

"Those who loved Rence Kelly in 'Polly with a Past' will love her even more as this frank, fresh young
girl from the chorus, who speaks her mind and speaks it quickly, and who, although she 'doesn't come
out of the top drawer,' as she says, is pure gold through and through."

The Phrase Finder mentions an earlier recording that is seen in the book The Hill, a Romance of Friendship by Horace Vachell, 1905:

"You'll find plenty of fellows abusing Harrow," he said quietly; "but take it from me, that the fault lies
not in Harrow, but in them. Such boys, as a rule, do not come out of the top drawer."

Reference: ThePhraseFinder, The Facts on File Encyclopedia of Word and Phrase Origins
* In the sport of basketball, there are many players who are considered to be top drawer when it comes to their handling on the ball.
Note: What you'll hear most of the time when it comes to identifying a phrase's origins are theories, rather than concrete facts. The reason? Because the origins cannot be understood well enough due to certain limitations. For example, when determining how old a phrase is, one can only go by what is written in old books, poems, newspapers, etc. So even if a phrase is written down in an old book, it was probably being used before it was even recorded.

However, old recordings do serve as a good indicator for when trying to discern the potential age of an expression. I try to find the oldest quotes available that contain the phrase, but keep in mind that there's always the  possibility for older forms existing that I may have missed. Thanks!
Picture for the expression Top Drawer.
A dresser with drawers!