We have cross-correlated X-ray catalogs derived from archival Chandra X-Ray Observatory ACIS observations with a Sloan Digital Sky Survey Data Release 2 (DR2) galaxy catalog to form a sample of 42 serendipitously X-ray-detected galaxies over the redshift interval 0.03<z<0.25. This pilot study will help fill in the ``redshift gap'' between local X-ray-studied samples of normal galaxies and those in the deepest X-ray surveys. Our chief purpose is to compare optical spectroscopic diagnostics of activity (both star formation and accretion) with X-ray properties of galaxies. Our work supports a normalization value of the X-ray-star formation rate correlation consistent with the lower values published in the literature. The difference is in the allocation of X-ray emission to high-mass X-ray binaries relative to other components, such as hot gas, low-mass X-ray binaries, and/or active galactic nuclei (AGNs). We are able to quantify a few pitfalls in the use of lower resolution, lower signal-to-noise ratio optical spectroscopy to identify X-ray sources (as has necessarily been employed for many X-ray surveys). Notably, we find a few AGNs that likely would have been misidentified as non-AGN sources in higher redshift studies. However, we do not find any X-ray-hard, highly X-ray-luminous galaxies lacking optical spectroscopic diagnostics of AGN activity. Such sources are members of the ``X-ray-bright, optically normal galaxy'' (XBONG) class of AGNs.