We present Monte Carlo calculations of the thermodynamics of the (2+1)-dimensional Thirring model at finite density. We bypass the sign problem by deforming the domain of integration of the path integral into complex space in such a way as to maximize the average sign within a parameterized family of manifolds. We present results for lattice sizes up to 10^{3} and we find that at high densities and/or temperatures the chiral condensate is abruptly reduced.