We discuss the results of a multi-wavelength differential imaging lab experiment with the High Contrast Imaging Testbed (HCIT) at the Jet Propulsion Laboratory. The HCIT combines a Lyot coronagraph with a Xinetics deformable mirror in a vacuum environment to simulate a space telescope in order to test technologies and algorithms for a future exoplanet coronagraph mission. At present, ground based telescopes have achieved significant attenuation of speckle noise using the technique of spectral differential imaging (SDI). We test whether ground-based SDI can be generalized to a non-simultaneous spectral differential imaging technique (NSDI) for a space mission. In our lab experiment, a series of 5 filter images centered around the O2(A) absorption feature at 0.762 um were acquired at nominal contrast values of 10^-6, 10^-7, 10^-8, and 10^-9. Outside the dark hole, single differences of images improve contrast by a factor of ~6. Inside the dark hole, we found significant speckle chromatism as a function of wavelength offset from the nulling wavelength, leading to a contrast degradation by a factor of 7.2 across the entire ~80 nm bandwidth. This effect likely stems from the chromatic behavior of the current occulter. New, less chromatic occulters are currently in development; we expect that these new occulters will resolve the speckle chromatism issue.