Domitian and the Christians
But during the reign of the Emperor Domitian, in the 90s AD, some people at court were killed for being "atheists", which means not believing in the gods. Suetonius does not use the word Christian, but to a Roman maybe the Christians seemed to not believe in the gods (after all they didn't believe in the Roman gods). One of the people killed was named Stephen, which is a Christian name.
The main thing we can gather from this information is that apparently Christianity itself was not yet illegal at this time, but nobody really knows whether Domitian ever killed people for being Christians or not.