Democritus, a greek philosopher, postulated that if you broke something in half, then in half again, and continued to do this ad infinitum, you'd end up with a particle that couldn't be divided any more. He called this particle an atom. But he didn't discover the atom, only postulated its existence. That was in 460 B.C.
Or was it his teacher? Democritus was a student of Leucippus and co-originator of the belief that all matter is made up of various imperishable indivisible (or perhaps undivided) elements.
They (or he) did call them "atomos" which apparently is an ancient Greek word meaning 'uncuttable'.