Yuri Gagarin is widely considered the first man to talk in space.
While the exact content of his initial vocalizations during his 1961 Vostok 1 flight might be debated due to recording limitations, it's almost certain that he spoke during his orbit. Gagarin's mission marked the beginning of human spaceflight, and communication was a critical part of the undertaking.
It is highly probable that he communicated with ground control during his orbit, thus making him the first man to talk in space.