The volatile abundances in comet 17P/Holmes were measured on three dates (UT 2007 October 27.6 and 31.3 and November 2.3) using high-dispersion (λ/Δ λ ~ 2.5 × 104) infrared spectroscopy with NIRSPEC at the W. M. Keck Observatory and CSHELL at the NASA Infrared Telescope Facility. Compared to other comets, the relative gas production rates in the coma show an enhancement of C2H6, HCN, and C2H2 with respect to H2O, by factors of ~2-3. CH3OH was also detected with an abundance relative to H2O that is similar to or perhaps slightly enhanced compared to the values observed in other comets. The apparent enrichment of some volatiles in the coma of 17P/Holmes does not necessarily imply an unusual composition for its nucleus because fractionation effects may be important at the relatively large heliocentric distance (Rh = 2.45 AU) at which our observations were performed. Rotational temperatures were determined for H2O, HCN, C2H6, and C2H2 in the coma on UT October 27.6 and found to be between 60 and 80 K. We used lines in both the ν5 and ν7 bands to obtain the best constraints yet achieved for the rotational temperature of C2H6. The spatial distributions of all measured volatiles in the coma are consistent with each other and suggest at most only a minor contribution from sublimating icy grains within our aperture. The overall gas production rate declined by approximately a factor of 7 between UT October 27.6 and November 2.3 with no significant change measured in the relative production rates of C2H6 and H2O during this time.