Thermochemical equilibrium calculations of gas abundances and condensation cloud formation are used to model the atmospheric chemistry of Gliese 229B. The calculations, which are analogous to our prior modeling of atmospheric chemistry of the Jovian planets in our solar system, predict the abundances of gases that are potentially observable by Earth-based and Earth-orbital telescopes. The calculations indicate that refractory elements such as Ca, Al, Ti, V, the lanthanides, Mg, Si, and Fe are removed by condensate cloud formation at temperatures above 1600 K and that gases containing these elements should not be observed. The major H, O, C, N, S, P, Cl, and F gases are predicted to be H2, H2O, CO (temperatures T > 1470 K), CH4 (T < 1470 K), N2 (T > 630 K), NH3 (T < 630 K), H2S, PH3 (T > 1155 K), P4O6 (T < 1155 K), HCl, and HF. By analogy with the Jovian planets in our solar system, we expect that rapid vertical mixing may quench the destruction of species such as CO, N2, HCN, and PH3, leading to abundances greater than thermochemical equilibrium values at low temperatures in the atmosphere of Gliese 229B. In principle, observations of CO, N2, the NH3/CH4 ratio, HCN, and PH3 could constrain such rapid vertical mixing and current models of the atmospheric thermal profile.