We investigate the phase diagram of the two-dimensional t-J model usin
g a recently developed Green's function Monte Carlo method for lattice
fermions. We use the technique to calculate exact ground-state energi
es of the model on large lattices. In contrast to many previous studie
s, we find the model phase separates for all values of J/t. In particu
lar, it is unstable at the hole dopings and interaction strengths at w
hich the model was thought to describe the cuprate superconductors.