In this paper we prove symmetry for solutions to the semi-linear elliptic equation Δu = f(u) in B1, 0 ≤ u < M, in B1, u = M, on ∂B1, where M > 0 is a constant, and B1 is the unit ball. Under certain assumptions on the r.h.s. f(u), the C1-regularity of the free boundary ∂{u > 0} and a second order asymptotic expansion for u at free boundary points, we derive the spherical symmetry of solutions. A key tool, in addition to the classical moving plane technique, is a boundary Harnack principle (with r.h.s.) that replaces Serrin’s celebrated boundary point lemma, which is not available in our case due to lack of C2-regularity of solutions.