Can a store ban me from entering?

There's a little convenience store near my house that has unwrapped Slim Jim Beef Sticks in a jar on the counter. The other day when I was in there, I slipped some Pupperoni dog treat sticks in there that look identical. The next time I was in there buying a soda, the owner told me he had me on tape 'tapering with the product' and that I was banned from the store. He claims a customer ate a portion of one of the dog treats and got ill. Is he legally allowed to ban me from a public place? I'm a paying customer.