That may seem like a really stupid question, and indeed it may in fact be, but the answer is far more interesting then you may think. Then again, maybe not.
No, not that Georgia.
What fascinates me about Button, other then his oddly adorable first name, was that he was the least important person do something amazing. He is an inspiration to those of use who want to sneak in at the last minute and pretend like we helped.
Gwinnett County in Georgia is named after Button
Button would sadly be killed in a duel by Lachlan McIntosh, a man even more obscure then Button himself.
Obscurity does have its advantages though. Apparently, there is a sub-culture of incredibly rich history buffs who collect Declaration of Independence. Having all the signatures is the Holy Grail of signature collecting. Because of his obscurity, Button's signature is the hardest to find. Therefore, Button's autograph is the most valuable autograph in the entire world. So Button is essentially famous for being obscure. That is truly a unique paradox.
If you would like to visit Button he is buried in Savannah Georgia's Colonial Cemetery
Although if you read the fine print on the Monument it says that Button is "believed to be buried somewhere in this area." Button was so obscure that no one even bothered to remember where he was buried.
Oh yeah, they also tore down his water tower.
So is the sad saga of Button Gwinnett.