We report resistivity-versus-temperature measurements performed on polycrystalline pellets of YBa2(Cu1-xMgx)3O7-δ made using the polymer-metal-complex precursor method. Tc was found to decrease linearly with increasing Mg doping in the range x=8.6×10-4 to 8.6×10-3 with slope -1400 K/x; the normal-state resistivity and the superconducting transition width showed little or no change. Mg was found to have a maximum solubility in YBa2(Cu1-xMgx)3O7-δ of x~=9×10-3.