Observations of the Seyfert 2 and starburst galaxy NGC 7130 with the Chandra X-ray Observatory illustrate that both of these phenomena contribute significantly to the galaxys detectable X-ray emission. The active galactic nucleus (AGN) is strongly obscured, buried beneath column density N_H > 10^{24} cm^{-2}, and it is most evident in a prominent Fe K alpha emission line with equivalent width greater than 1 keV. The AGN accounts for most (60%) of the observed X-rays at energy E > 2 keV, with the remainder due to spatially extended star formation. The soft X-ray emission is strong and predominantly thermal, on both small and large scales. We attribute the thermal emission to stellar processes. In total, the AGN is responsible for only one-third of the observed 0.5--10 keV luminosity of 3 x 10^{41} erg/s of this galaxy, and less than half of its bolometric luminosity. Starburst/AGN composite galaxies like NGC 7130 are truly common, and similar examples may contribute significantly to the high-energy cosmic X-ray background while remaining hidden at lower energies, especially if they are distant.