We present new measurements of a thermodynamic property, the mass density, and of a transport property, the shear viscosity, of a solution of linear poly(alpha -methylstyrene), with a number average molecular weight of 32 300, in the solvent methylcyclohexane, in the one and two phase regions within 3 K of the liquid-liquid critical temperature, T-c. Both the density and the viscosity were measured with a magnetic suspension densimeter/rheometer, with precisions of 56 ppm and 4%, respectively. We find no critical anomalies in the density above T-c, the average density below T-c, the viscosity above T-c, or the average viscosity below T-c. The behavior of the difference in density below T-c is consistent with the Ising model.