Yes, the word "chit" originated with the British in India. It means a small slip of paper used as a note or receipt:
"Give me the chit from the cleaners, and I'll pick up your coat on the way home from church."
"Take this chit over to Debbie, and bring it back with an answer."
Mark Steyn gave a list of other words with the same origin.
The word "chit" is used alot in the Navy. Special Request chit, leave chit, etc.