The QCD Phase Diagram for Three Degenerate Flavors and Small Baryon Density

We present results for the phase diagram of three flavor QCD for \mu_B ~ 500 MeV. Our simulations are performed with imaginary chemical potential \mu_I 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. Our results for the endpoint differ significantly from those obtained by other methods, and we discuss possible reasons for this.