  We present multi-epoch, $R-$band imaging obtained from the Palomar Transient
Factory of a small, fan-shaped reflection nebula in NGC 1333 that experiences
prominent brightness fluctuations. Photometry of HBC 340 (K7e) and HBC 341
(M5e), a visual pair of late-type, young stellar objects lying near the apex of
the nebula, demonstrates that while both are variable, the former has
brightened by more than two magnitudes following a deep local minimum in
September 2014. Keck high dispersion (R$\sim$45,000-66,000), optical
spectroscopy of HBC 340 suggests that the protostar is a spectroscopic binary
(HBC 340Aa + HBC 340Ab). Both HBC 340 and HBC 341 exhibit strong H$\alpha$ and
forbidden line emission, consistent with accretion and outflow. We conclude
that the brightness fluctuations in the reflection nebula represent light echos
produced by varying incident radiation emanating from HBC 340. The short-term
variability observed in the protostar is attributed to irregular accretion
activity, while correlated, dipping behavior on a several hundred day time
scale may be due to eclipse-like events caused by orbiting circumstellar
material. Archival Hubble Space Telescope imaging of the region reveals a
second, faint (F814W$\sim$20.3 mag) companion to HBC 340 that lies 1.02"
($\sim$235 AU) east of the protostar. If associated, this probable substellar
mass object (20-50 Jupiter masses), HBC 340B, is likely unrelated to the
observed brightness variations. The sustained brightening of HBC 340 since late
2014 can be explained by an EXor-like outburst, the recovery from a long
duration eclipse event caused by obscuring circumstellar dust, or by the
gradual removal of extincting material from along the line of sight. Our
analysis here favors one of the extinction scenarios.
