We have studied via Green-function Monte Carlo (GFMC) technique the S=(1/2 Heisenberg quantum antiferromagnet in two dimensions on a square lattice. GFMC is a T=0 stochastic method that projects out the component of the ground state in a given variational wave function. From studies on lattices up to 12×12, we find the ground-state energy per site E0/J=-0.6692(2). We include the zero-point motion of the elementary excitations in the ground state and show that it produces long-range correlations in the wave function. We obtain a staggered magnetization m°=0.31(2) in units in which the classical Néel state is 0.5. The structure factor at long wavelengths is S(q)~q and from the slope we deduce the spin-wave velocity.