Of the highest quality, importance, or rank, as in The musicians in this pick-up orchestra were top drawer. It probably alludes to the uppermost drawer in a bureau or chest, where the most valuable objects (such as jewelry) are usually kept. [c. 1900]
Highest quality. The 19th-century practice of keeping jewelry and other valuables in the highest drawer of a bedroom dresser gave rise to this phrase, which was applied both to people and to things. “First rate” is a similar phrase, as is “varsity,” meaning a person figuratively sufficiently admirable to qualify for the starting team.