  The Kepler mission has provided a wealth of data, revealing new insights in
time-domain astronomy. However, Kepler's single band-pass has limited studies
to a single wavelength. In this work we build a data-driven, pixel-level model
for the Pixel Response Function (PRF) of Kepler targets, modeling the image
data from the spacecraft. Our model is sufficiently flexible to capture known
detector effects, such as non-linearity, intra-pixel sensitivity variations,
and focus change. In theory, the shape of the Kepler PRF should also be weakly
wavelength dependent, due to optical chromatic aberration and wavelength
dependent detector response functions. We are able to identify these predicted
shape changes to the PRF using the residuals between Kepler data and our model.
In this work, we show that these PRF changes correspond to wavelength
variability in Kepler targets using a small sample of eclipsing binaries. Using
our model, we demonstrate that pixel-level light curves of eclipsing binaries
show variable eclipse depths, ellipsoidal modulation and limb darkening. These
changes at the pixel level are consistent with multi-wavelength photometry. Our
work suggests each pixel in the Kepler data of a single target has a different
effective wavelength, ranging from $\approx$ 550-750 $nm$. In this proof of
concept, we demonstrate our model, and discuss possible use cases for the
wavelength dependent Pixel Response Function of Kepler. These use cases include
characterizing variable systems, and vetting exoplanet discoveries at the pixel
level. The chromatic PRF of Kepler is due to weak wavelength dependence in the
optical systems and detector of the telescope, and similar chromatic PRFs are
expected in other similar telescopes, notably the NASA TESS telescope.
