  We present the discovery of seven new proplyds (i.e. sources surrounded by
cometary Halpha emission characteristic of offset ionization fronts) in NGC
1977, located about 30' north of the Orion Nebula Cluster at a distance of ~400
pc. Each of these proplyds are situated at projected distances 0.04-0.27 pc
from the B1V star 42 Orionis (c Ori), which is the main source of UV photons in
the region. In all cases the ionization fronts of the proplyds are clearly
pointing toward the common ionizing source, 42 Ori, and 6 of the 7 proplyds
clearly show tails pointing away from it. These are the first proplyds to be
found around a B star, with previously known examples instead being located
around O stars, including those in the Orion Nebula Cluster around $\theta^1$
Ori C. The radii of the offset ionization fronts in our proplyds are between
~200 and 550 AU; two objects also contain clearly resolved central sources that
we associate with disks of radii 50-70 AU. The estimated strength of the FUV
radiation field impinging on the proplyds is around 10-30 times less than that
incident on the classic proplyds in the Orion Nebula Cluster. We show that the
observed proplyd sizes are however consistent with recent models for FUV
photoevaporation in relatively weak FUV radiation fields.
