  We report the results of a new experimental search for a permanent electric
dipole moment of 199Hg utilizing a stack of four vapor cells. We find d(199Hg)
= (0.49 \pm 1.29_stat \pm 0.76_syst) x 10^{-29} e cm, and interpret this as a
new upper bound, |d(199Hg)| < 3.1 x 10^{-29} e cm (95% C.L.). This result
improves our previous 199Hg limit by a factor of 7, and can be used to set new
constraints on CP violation in physics beyond the standard model.
