Nothing but your merchant agreement. I worked a register in a small store when I was 16, and in a slow moment I ended up reading some of the stuff VISA sent along with their booklet of invalid credit card numbers. (Yes, this was a while ago.)
In in the fine print it was clear that offering your customers a cash discount was grounds for immediately canceling your ability to take credit cards. If I recall rightly, I noticed because the store I was at did indeed offer a discount. In practice, I'm sure the store was small enough that VISA didn't care. But for larger operations I'm sure it was a serious threat.
I believe they were eventually sued and lost, but since I rarely see discounts like that, I imagine they have some sort of not-quite-illegal trick, like offering merchants advertising credits based on charged card volume.
In in the fine print it was clear that offering your customers a cash discount was grounds for immediately canceling your ability to take credit cards. If I recall rightly, I noticed because the store I was at did indeed offer a discount. In practice, I'm sure the store was small enough that VISA didn't care. But for larger operations I'm sure it was a serious threat.
I believe they were eventually sued and lost, but since I rarely see discounts like that, I imagine they have some sort of not-quite-illegal trick, like offering merchants advertising credits based on charged card volume.