We obtained high resolution (λ/δλ ∼ 10,000-20,000) infrared (IR) spectra of Comet 21P/Giacobini-Zinner (GZ) at five different wavelengths between 1.9 and 5.0 µm during 25-29 October 1998 using CSHELL at the NASA Infrared Telescope Facility (IRTF) on Mauna Kea. We also obtained a moderate resolution (λ/δλ ∼ 680) spectrum covering the wavelength range from 3.082 to 3.720 µm on 29 October 1998 using CGS4 at the United Kingdom Infrared Telescope (UKIRT) on Mauna Kea. Five rovibrational lines in three different vibrational bands of H 2 O were detected in the CSHELL spectra. Assuming that the rotational temperature was ∼50 K, we derive a H 2 O production rate of ∼2-3 × 10 28 molecules s -1 , which is ∼2 times smaller than the value derived from nearly simultaneous radio observations of OH. After continuum subtraction, the CGS4 spectrum displays significant excess flux that we attribute mainly to CH 3 OH fluorescence, and we derive that the CH 3 OH production rate was ∼2.7 × 10 26 molecules s -1 . The corresponding CH 3 OH/H 2 O relative abundance is ∼0.9-1.4%, which falls within the range of values observed in other comets, albeit at the low end. The CGS4 spectrum also has significant excess flux near 3.43 µm that is not explained by our CH 3 OH fluorescence model; a similar feature has been observed in several other comets, but its origin remains a mystery. We did not detect any excess emission near 3.28 µm, where some comets show a feature that may be associated with polycyclic aromatic hydrocarbons. We also searched for emissions from C 2 H 6 , CO, HCN, C 2 H 2 , and H 2 CO but did not detect any of these molecules. The 3σ upper limits for the abundances relative to H 2 O are 0.05-0.08% for C 2 H 6 , 2-3% for CO, 0.2-0.3% for HCN, 0.3-0.4% for C 2 H 2 , and 0.5-0.8% for H 2 CO, assuming that all species are parent molecules and that their rotational temperature in the coma is 50 K. C 2 H 6 is depleted by a factor of ∼15 or more compared to its relative abundance in Comets Hale-Bopp 482