Hi there! As Cooper pointed out, I'm Sara. And yes, Tribbles reproduce like...well Tribbles honestly. They're born pregnant, as was explained, and are hermaphroditic to boot. So they don't even need a mate to reproduce. They can also have litters of up to ten, so yeah.
One is fine. Sadly that one is never just one. We're figuring out how to solve the problem. Trust me, I'm planning on keeping one myself.