Subarcsecond radio continuum observations of the Galactic center region at lambda = 6 and 2 cm reveal a 0."5 diameter source with a shell-like morphology. This source is linearly polarized at a level of 16% at 6 cm and has a steep nonthermal spectrum with a spectral index of 1.6 between 6 and 2 cm. The distance to this source is not known, but the large rotation measure value of 3000 rad m ^{-2} suggests that G359.87+0.18 is likely to be located in the inner Galaxy or at an extragalactic distance. We discuss possible interpretations of this object as a recent supernova, a very young supernova remnant, a nova remnant, or an extragalactic source. All possibilities are highly problematic.