HHeF, a chemically-bound helium compound, has been predicted to be metastable in the gas phase. It decays by tunneling through energy barriers in picosecond timescales into He+HF and H+He+F. This paper studies the stability of HHeF in pressurized solid helium. Using realistic potentials for the HHeF/He interaction, the potential energy along the minimum energy paths for decomposition is evaluated, and tunneling decay times are computed by the WKB approximation. It is found that for pressures above 500 MPa, decomposition into H+He+F is completely suppressed. At 23 GPa, the highest pressure studied, the timescale for HHeF→He+HF is in the millisecond range. At pressures well above 23 GPa, HHeF is thus expected to remain stable indefinitely.