  We report first results from the Cryogenic Dark Matter Search (CDMS II)
experiment running with its full complement of 30 cryogenic particle detectors
at the Soudan Underground Laboratory. This report is based on the analysis of
data acquired between October 2006 and July 2007 from 15 Ge detectors (3.75
kg), giving an effective exposure of 121.3 kg-d (averaged over recoil energies
10--100 keV, weighted for a weakly interacting massive particle (WIMP) mass of
60 \gev). A blind analysis, incorporating improved techniques for event
reconstruction and data quality monitoring, resulted in zero observed events.
This analysis sets an upper limit on the WIMP-nucleon spin-independent cross
section of 6.6$\times10^{-44}$ cm$^2$ (4.6$\times10^{-44}$ cm$^2$ when combined
with previous CDMS Soudan data) at the 90% confidence level for a WIMP mass of
60 \gev. By providing the best sensitivity for dark matter WIMPs with masses
above 42 GeV/c$^2$, this work significantly restricts the parameter space for
some of the favored supersymmetric models.
