This paper presents BVR CCD surface photometry of NGC 7187, a southern S0+ galaxy possessing a bright circular inner ring and a faint elongated outer ring. The rings both have a contrast comparable to those observed in typical (R)SB(r)-type galaxies, yet there is no obvious bar crossing the inner ring as in such galaxies. Instead, there are two nearly orthogonal, small oval zones in the bulge region, one of which may be a nuclear bar. The inner ring is a narrow zone of slightly enhanced blue colors and is therefore a place where star formation has been favored in the disk. An asymmetry in the outer ring region suggests that the galaxy has suffered some interaction, possibly associated with membership in a group whose mean redshift is 2500 km s-1. The origin of the two rings is uncertain. If they are resonance rings, then NGC 7187 would be a possible example of a galaxy which once had a stronger, more important bar than it has now. This bar could have evolved to a more axisymmetric state through an internal interaction, leaving the rings and an inner lens as signatures of its presence. However, the data do not exclude completely the possibility that both rings are a result of a collision or merger/accretion of one or more smaller galaxies with an S0, in which case NGC 7187 would more properly belong into the pure ring galaxy or Hoag-type ring galaxy classes. The main argument against this possibility is that NGC 7187 does not resemble the more prototypical members of those classes. Other considerations are discussed in some detail.