  We report the first results from a search for weakly interacting massive
particles (WIMPs) in the Cryogenic Dark Matter Search (CDMS) experiment at the
Soudan Underground Laboratory. Four Ge and two Si detectors were operated for
52.6 live days, providing 19.4 kg-d of Ge net exposure after cuts for recoil
energies between 10--100 keV. A blind analysis was performed using only
calibration data to define the energy threshold and selection criteria for
nuclear-recoil candidates. Using the standard dark-matter halo and
nuclear-physics WIMP model, these data set the world's lowest exclusion limits
on the coherent WIMP-nucleon scalar cross-section for all WIMP masses above 15
GeV, ruling out a significant range of neutralino supersymmetric models. The
minimum of this limit curve at the 90% C.L. is 4 x 10^{-43} cm^2 at a WIMP mass
of 60 GeV.
