Presently, the Stark effect contributes the largest source of uncertainty in a ytterbium optical atomic clock through blackbody radiation. By employing an ultracold, trapped atomic ensemble and high stability optical clock, we characterize the quadratic Stark effect with unprecedented precision. We report the ytterbium optical clock's sensitivity to electric fields (such as blackbody radiation) as the differential static polarizability of the ground and excited clock levels α(clock) = 36.2612(7) kHz (kV/cm)(-2). The clock's uncertainty due to room temperature blackbody radiation is reduced by an order of magnitude to 3×10(-17).