We present new Chandra observations that complete a sample of seventeen ( 17 ) luminous infrared galaxies ( LIRGs ) with D < 60 Mpc and low Galactic column densities of N _ { H } \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 5 \times 10 ^ { 20 } cm ^ { -2 } . The LIRGs in our sample have total infrared ( 8–1000 \mu m ) luminosities in the range of L _ { IR } \approx ( 1–8 ) \times 10 ^ { 11 } L _ { \odot } . The high-resolution imaging and X-ray spectral information from our Chandra observations allow us to measure separately X-ray contributions from active galactic nuclei ( AGNs ) and normal galaxy processes ( e.g. , X-ray binaries and hot gas ) . We utilized total infrared plus UV luminosities to estimate star-formation rates ( SFRs ) and K -band luminosities and optical colors to estimate stellar masses ( M _ { \star } ) for the sample . Under the assumption that the galaxy-wide 2–10 keV luminosity ( L _ { HX } ^ { gal } ) traces the combined emission from high mass X-ray binaries ( HMXBs ) and low mass X-ray binaries ( LMXBs ) , and that the power output from these components are linearly correlated with SFR and M _ { \star } , respectively , we constrain the relation L _ { HX } ^ { gal } = \alpha M _ { \star } + \beta { SFR } . To achieve this , we construct a Chandra -based data set composed of our new LIRG sample combined with additional samples of less actively star-forming normal galaxies and more powerful LIRGs and ultraluminous infrared galaxies ( ULIRGs ) from the literature . Using these data , we measure best-fit values of \alpha = ( 9.05 \pm 0.37 ) \times 10 ^ { 28 } ergs s ^ { -1 } M _ { \odot } ^ { -1 } and \beta = ( 1.62 \pm 0.22 ) \times 10 ^ { 39 } ergs s ^ { -1 } ( M _ { \odot } yr ^ { -1 } ) ^ { -1 } . This scaling provides a more physically meaningful estimate of L _ { HX } ^ { gal } , with \approx 0.1–0.2 dex less scatter , than a direct linear scaling with SFR . Our results suggest that HMXBs dominate the galaxy-wide X-ray emission for galaxies with SFR/ M _ { \star } \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 5.9 \times 10 ^ { -11 } yr ^ { -1 } , a factor of \approx 2.9 times lower than previous estimates . We find that several of the most powerful LIRGs and ULIRGs , with SFR/ M _ { \star } \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 10 ^ { -9 } yr ^ { -1 } , appear to be X-ray underluminous with respect to our best-fit relation . We argue that these galaxies are likely to contain X-ray binaries residing in compact star-forming regions that are buried under thick galactic columns large enough to attenuate emission in the 2–10 keV band ( N _ { H } \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 10 ^ { 23 } cm ^ { -2 } ) .