Interesting discussion on Reddit. Two answers:
Bone needles and scraped skins found in archeological digs suggest we started wearing clothes 100,000 to 500,000 years ago.
Body lice suggest a date of 100,000 years ago. Unlike other primates, human beings have different, but related, kinds of lice: One for the head, and one for the body. Head lice live in hair, and body lice live in clothes. The lice diverged about 100,000 years ago.
A hundred thousand years of evolution — and now people can’t wait to get home from work so they can take off their pants.