© 2016. The American Astronomical Society. All rights reserved..Our current understanding of galaxy evolution still has many uncertainties associated with the details of the accretion, processing, and removal of gas across cosmic time. The next generation of radio telescopes will image the neutral hydrogen (H i) in galaxies over large volumes at high redshifts, which will provide key insights into these processes. We are conducting the COSMOS H i Large Extragalactic Survey (CHILES) with the Karl G. Jansky Very Large Array, which is the first survey to simultaneously observe H i from z = 0 to z ~ 0.5. Here, we report the highest redshift H i 21 cm detection in emission to date of the luminous infrared galaxy COSMOS J100054.83+023126.2 at z = 0.376 with the first 178 hr of CHILES data. The total H i mass is (2.9 ± 1.0) × 1010 M o and the spatial distribution is asymmetric and extends beyond the galaxy. While optically the galaxy looks undisturbed, the H i distribution suggests an interaction with a candidate companion. In addition, we present follow-up Large Millimeter Telescope CO observations that show it is rich in molecular hydrogen, with a range of possible masses of (1.8-9.9) × 1010 M o. This is the first study of the H i and CO in emission for a single galaxy beyond z ~ 0.2.