That would be a "taxi receipt" in AE, I think. A "taxi chit" would be more likely to be a slip of paper that the taxi driver would take as payment, issued by your employer (for example, to get you home if you had to work late into the evening).
So the answer may depend on whether it's a BE or AE context.
In AE we would call them vouchers, and they are indeed pieces of paperwork used as payment for rides. They can look like a governmental form, like the ones the Job Corps uses to compensate cab companies for hauling their people on furlough. Or they can be more like coupons.
When I drove cab, we had a program called "Home Free," and the tavern owners participated-- I guess they got a discount on their liability insurance. When a bar patron got too drunk to drive, the tapmeister commandeered his car keys and called us up.
Sometimes he would do this without making sure the drunk understood what was happening, and these were the "fun" kind of calls we almost wished didn't come our way (desperate as we were for work). The bartender gave us the voucher and showed us the car keys to prove the guy had a car, and he wasn't just using the cab service to rid himself of some bum who'd wandered in. We were supposed to get a look at the keys, anyway-- like I said, our desperation for a paycheck was a disincentive against enforcing other people's rules.
If you ever find yourself using a "taxi chit" or voucher of any kind, by the way, please don't "conveniently forget" that these things don't cover tips. We know where you live. .
Taxi chit is definitely used here. These are normally small cards with the address and phone number of the cab firm on them. On the back, the driver writes the date, the fare, where the journey started and finished.
"Chit" is not often used to refer to a specific item in AE. It usually is more abstract meaning something that is a proxy for money, especially those only valid in specific places or communities. However, in certain places, different words have become more common. "Points" are often dollar-for-dollar debits from a prearranged accounts on college campuses to pay for food, laundry, photocopies, and so on. These are encoded on the student's identification card and more convenient than carrying money with you all around. "Cupons" more often refers to physical objects, pieces of paper, that are to be redeemed only for an item stated on them, or a discount on that item. If you hear about "checks [BE ticks]", "punches", or "stamps", these reference the method that cards distributed by businesses are marked. These cards usually offer a free item after a given number have been purchased. This is a way to get the costomer to return to the store, of course.
A taxi chit is payment voucher that people (companies) use to pay for taxis in lieu of cash. This is very convenient for companies because companies do not have to use their petty cash every time a staff needs a taxi to go to a meeting. I work for a big university and every day, we have about 20 to 30 people going out for meetings so we use taxi chits from one of the local taxi companies.