  As the only directly imaged multiple planet system, HR 8799 provides a unique
opportunity to study the physical properties of several planets in parallel. In
this paper, we image all four of the HR 8799 planets at H-band and 3.3 microns
with the new LBT adaptive optics system, PISCES, and LBTI/LMIRCam. Our images
offer an unprecedented view of the system, allowing us to obtain H and 3.3$
micron photometry of the innermost planet (for the first time) and put strong
upper-limits on the presence of a hypothetical fifth companion. We find that
all four planets are unexpectedly bright at 3.3 microns compared to the
equilibrium chemistry models used for field brown dwarfs, which predict that
planets should be faint at 3.3 microns due to CH4 opacity. We attempt to model
the planets with thick-cloudy, non-equilibrium chemistry atmospheres, but find
that removing CH4 to fit the 3.3 micron photometry increases the predicted L'
(3.8 microns) flux enough that it is inconsistent with observations. In an
effort to fit the SED of the HR 8799 planets, we construct mixtures of cloudy
atmospheres, which are intended to represent planets covered by clouds of
varying opacity. In this scenario, regions with low opacity look hot and
bright, while regions with high opacity look faint, similar to the patchy cloud
structures on Jupiter and L/T transition brown-dwarfs. Our mixed cloud models
reproduce all of the available data, but self-consistent models are still
necessary to demonstrate their viability.
