We used the ROSAT Position Sensitive Proportional Counter (PSPC) to obtain a 13 ks exposure and the ROSAT HRI to obtain a 42.5 ks exposure of the faint S0 galaxy NGC 1380. We show that the PSPC spectrum can be modeled as a thermal spectrum with kT ~ 0.5 keV, which is consistent with emission from a hot interstellar medium. We do not detect any emission from a hard component; the 90% upper limit is consistent with the trend for the scaled-up luminosities of X-ray-emitting point sources. The radial profiles from the PSPC and HRI data support the spectral fitting, because each profile is more sharply concentrated than the optical light (which reflects the stellar distribution), in contrast to other E/S0 galaxies. The PSPC radial profile is consistent with emission from a point source, because of the larger point-spread function; the HRI profile reveals the presence of extended hot gas. We also extend the L_X-L_B plane, described by Matsumoto et al. in the range 10.8 < log L_B < 11.3, to log L_B ~ 10.5. We extend this plane separately for the hard discrete and the soft thermal components and show that the scaling relation for the hard component continues to at least log L_B ~ 10.5.