  We report the results of a high-spatial-resoltion search for the progenitor
of type Ic supernova SN 2004gt, using the newly commissioned Keck laser-guide
star adaptive optics system (LGSAO) along with archival Hubble Space Telescope
data. This is the deepest search yet performed for the progenitor of any type
Ib/c event in a wide wavelength range stretching from the far UV to the near
IR. We determine that the progenitor of SN 2004gt was most likely less luminous
than M_V=-5.5 and M_B=-6.5 magnitudes. The massive stars exploding as
hydrogen-deficient core-collapse supernovae (SNe) should have lost their outer
hydrogen envelopes prior to their explosion, either through winds -- such stars
are identified within our Galaxy as Wolf-Rayet (W-R) stars -- or to a binary
companion. The luminosity limits we set rule out more than half of the known
galactic W-R stars as possible progenitors of this event. In particular, they
imply that a W-R progenitor should have been among the more-evolved (highly
stripped, less luminous) of these stars, a concrete constraint on its
evolutionary state just prior to core collapse. The possibility of a less
luminous, lower-mass binary progenitor cannot be constrained. This study
demonstrates the power of LGS observations in furthering our understanding of
core collapse, and the physics powering supernovae, GRBs and XRFs.
