  We propose a new method to investigate the thermal properties of QCD with a
small quark chemical potential $\mu$. Derivatives of the phase transition point
with respect to $\mu$ are computed at $\mu=0$ for 2 flavors of p-4 improved
staggered fermions with $ma=0.1,0.2$ on a $16^3\times4$ lattice. The resulting
Taylor expansion is well behaved for the small values of $\mu_{\rm
q}/T_c\sim0.1$ relevant for RHIC phenomenology, and predicts a critical curve
$T_c(\mu)$ in reasonable agreement with estimates obtained using exact
reweighting. In addition, we contrast the case of isoscalar and isovector
chemical potentials, quantify the effect of $\mu\not=0$ on the equation of
state, and comment on the complex phase of the fermion determinant in QCD with
$\mu\not=0$.
