Three Galactic O-type stars belong to the rare class of Of? p objects: HD 108, HD 191612, and HD 148937. The first two stars show a wealth of phenomena, including strong X-ray emission, light variability, and dramatic periodic spectral variability. We present here the first detailed optical and X-ray study of the third Galactic Of? p star, HD 148937. Spectroscopic monitoring has revealed low-level variability in the Balmer and He II lambda 4686 lines, but constancy at He I and C III lambda 4650. The H alpha line exhibits profile variations at a possible periodicity of similar to 7 days. Model atmosphere fits yield T-eff = 41000 +/- 2000 K, log(g) = 4.0 +/- 0.1, M-sph less than or similar to 10(-7) M-circle dot yr(-1), and an overabundance of nitrogen by a factor of 4. At X-ray wavelengths, HD 148937 resembles HD 108 and HD 191612 in having a thermal spectrum dominated by a relatively cool component (kT = 0.2 keV), broad lines (>= 1700 km s(-1)), and an order-of-magnitude overluminosity compared to normal O stars (log[L-X(unabs) / L-BOL]similar to -6).