Queen Bee

Apologies if this has already been asked/answered. I just built my first beehive and I have 1 queen and 4 workers. I built the breeding chamber add on and see that the queen will produce a finite supply of workers before dying herself. Is there a way to reproduce queens? At a 33% respawn rate, it seems like a terrible game design to force us to keep hunting for hives w/ the hopes of finding additional queens. Am I missing something?