  Project 1640 is a high-contrast imaging instrument recently commissioned at
Palomar observatory. A combination of a coronagraph with an integral field
spectrograph (IFS), Project 1640 is designed to detect and characterize
extrasolar planets, brown dwarfs, and circumstellar material orbiting nearby
stars. In this paper, we present our data processing techniques for improving
upon instrument raw sensitivity via the removal of quasi-static speckles. Our
approach utilizes the chromatic image diversity provided by the IFS in
combination with the locally-optimized combination of images (LOCI) algorithm
to suppress the intensity of residual contaminating light in close angular
proximity to target stars. We describe the Project 1640 speckle suppression
pipeline (PSSP) and demonstrate the ability to detect companions with
brightness comparable to and below that of initial speckle intensities using
on-sky commissioning data. Our preliminary results indicate that suppression
factors of at least one order of magnitude are consistently possible, reaching
$5\sigma$ contrast levels of $2.1\times10^{-5}$ at $1\arcsec$ in the H-band in
20 minutes of on-source integration time when non-common-path errors are
reasonably well-calibrated. These results suggest that near-infrared contrast
levels of order $\approx10^{-7}$ at subarcsecond separations will soon be
possible for Project 1640 and similarly designed instruments that receive a
diffraction-limited beam corrected by adaptive optics (AO) systems employing
deformable mirrors with high actuator-density.
