We present results for the phase diagram of three-flavor QCD for $mu_B < 500$ MeV. Our simulations are performed with an imaginary chemical potential for which the fermion determinant is positive. Physical observables are then fitted by truncated Taylor series and continued to real chemical potential. We map out the location of the critical line $T_c(mu_B)$ with an accuracy up to terms of order $(mu_B/T)^6$. We also give first results on a determination of the critical endpoint of the transition and its quark mass dependence.