  We present single-crystal neutron scattering measurements of the spin-1/2
equilateral triangular lattice antiferromagnet Ba$_3$CoSb$_2$O$_9$. Besides
confirming that the Co$^{2+}$ magnetic moments lie in the ab plane for zero
magnetic field, we determine all the exchange parameters of the minimal
quasi-2D spin Hamiltonian, which confirms that Ba$_3$CoSb$_2$O$_9$ is an almost
perfect realization of the paradigmatic model of frustrated quantum magnetism.
A comparison with linear and nonlinear spin-wave theory reveals that quantum
fluctuations induce a strong downward renormalization of the magnon dispersion.
