My first ever post and I do not really know what I am doing but I did research the coin and I am pretty confident it is not counterfeit. The Red book says this is worth 25$ but of course this does not consider the hole.
I'm trying to figure out if it's struck off-center, or if that's just an optical illusion from your image.
Maybe slightly off center. I am not an expert, but there is listed a 1848 small date that is counterfeit.
Well, being struck off-center is good, not bad. In general, the more any coin's off-center, the more it's worth, all other things being equal. There are plenty of Large Cents around, and one with a hole is going to be relegated to a pocket piece of tiny numismatic value, although otherwise it's a nice example, a bit dark. Absolutely don't clean it or polish it, it's suffered enough. I can't recall ever seeing a counterfeit Large Cent. I've seen some that were re-tooled to pass for a rare die variety.
I think there was a post in another thread about Chinese counterfeit LC's. Some people actually collect holed coins, but to me this is a cull.
The coin is definitely off-center (my guess is 8-12 degrees). I have never noticed that but that is interesting. I do suspect my coin is close to worthless but it is the oldest coin I have and will cherish is for many years to come.
Michael K is right, I did post an image of a huge vat full of Chinese half cents, large cents, and Indians, but I have never seen one in person, in my hands. That's the difference.