  We report the results of magnetization and specific heat measurements on
Ba$_3$CoSb$_2$O$_9$, in which the magnetic Co$^{2+}$ ion has a fictitious
spin-1/2, and show evidence that a spin-1/2 Heisenberg antiferromagnet on a
regular triangular lattice is actually realized in Ba$_3$CoSb$_2$O$_9$. We
found that the entire magnetization curve including the one-third quantum
magnetization plateau is in excellent agreement with theoretical calculations
at a quantitative level.
