  The differential polarizability, due to near-infrared light at 1126 nm, of
the 27Al+ 1S0 -> 3P0 clock transition is measured to be 4\pi\epsilon_0 x (1.6
+/- 0.5) x 10^{-31} m^3. This measurement is combined with experimental
oscillator strengths to extrapolate the differential static polarizability of
the clock transition as 4\pi\epsilon_0 x (1.5 +/- 0.5) x 10^{-31} m^3. The
resulting room temperature blackbody fractional frequency shift of -8(3) x
10^{-18} is the lowest known shift of all atomic transitions under
consideration for optical frequency standards. A method is presented to
estimate the differential static polarizability of an optical transition, from
a differential light shift measurement.
