  We present the first results of a new search for a permanent electric dipole
moment of the ^{199}Hg atom using a UV laser. Our measurements give d(Hg)= -
(1.06 +/- 0.49 +/- 0.40) 10^{-28} e cm. We interpret the result as an upper
limit |d(Hg)| < 2.1 10^{-28} e cm (95% C.L.), which sets new constraints on
theta_{QCD}, chromo-EDMs of the quarks, and CP violation in Supersymmetric
models.
