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Analysis of high-resolution IR spectra of CH Cygni shows that the star is a triple system with a short period orbit of just over 2 yrs. The period ratio of seven for CH Cyg is the smallest known for a triple system. The symbiotic pair is the short-period system. An eccentric and a circular orbit solution are determined for the short-period pair, and the circular orbit solution is found to be more appropriate. The observed eccentricity appears to be due to phase-dependent line asymmetries resulting from the irradiation of the M giant by the white dwarf. The system does not eclipse. The most consistent mode of the system is a short-period pair consisting of an M6 giant of two solar masses that is within a factor of two of filling its Roche lobe and a white dwarf of 0.2 solar mass. The orbital inclination is about 70 deg. The unseen third star in the system is probably a G-K dwarf.