They put at least 31 nuclear fission reactors in Earth orbit to power
their spysats. And I mean reactors, not RTGs.

Lots of details here. You can see people are just chomping at the bit
to get real reactors out there.

http://www.world-nuclear.org/info/inf82.html

The big nuclear powers probably won't ever test a nuclear bomb in space
again. But if some other new nuclear power wanted to, would anyone
be able to stop them? Probably not some old UN treaty, to be sure. It
didn't stop the Chinese or India or Pakistan from doing above-ground
tests.

A nuclear reactor for a lunar base at its south pole makes sense, where
the Sun often never reaches. It's also good for Mars due to being about
twice as far from the Sun as Earth.