Why does my one-year-old kitten's urine smell so bad?

It could be your cats diet. Try this site.
http://planeturine.com/dsp_carpet.cfm

Well, ammonia is a natural component of urine, so it’s going to smell a little like it regardless. But if it seems unnaturally strong, my best guess would be a urinary tract infection.
Though, I’d assume your vet would have tested for that. Maybe explicitly ask your vet to test for UTI?

maybe it ate something rotten like a dead squirrel.

Has your kitten been fixed, i.e., neutered if male and spayed if female? If not, have it done. That will take care of the problem.

Could the cat be dehydrated? This would make the urine more concentrated, and thus smell worse.

@ Marina – I agree that sounds like the most likely cause. Has she had a cat before?

maybe the cat got into the asparagus drawer?

Thanks everyone! We scrubbed the litter box earlier today and added new litter and so far so good. Thanks for your advice!

Make sure your cat has a fresh supply of water at all times. As xyzzy says, the urine will smell worse if it is not diluted. Plus, it’s just healthier for her to have plenty of water to drink,

It a male!