It's your lock and the keys that came with it are yours as well, so the direct answer to your question is that you should be given one of the keys. (I'm assuming that the lock came with two keys).
However there's a counter argument: If the tenant originally had one key and then got another one cut for his partner (or cleaner, or whoever) then he shouldn't lose out financially through the failure of something which you're responsible for (i.e. the lock). So, if he returned your key, he would have a valid claim against you for the cost of getting another one cut for his partner/cleaner/whoever.
So, assuming that the tenant already had a spare key, he has the right to hold one now (at your expense). If (apart from this minor dispute) he's a good tenant, it's really not worth the hassle of arguing over it.