The column abundances of CH3 observed by the Infrared Space Observatory (ISO) satellite on Saturn and Neptune were lower than predicted by atmospheric photochemical models, especially for Saturn. It has been suggested that the models underestimated the loss of CH3 due to poor knowledge of the rate constant k of the CH3 + CH3 self-reaction at the low temperatures and pressures of these atmospheres. Motivated by this suggestion, we undertook a combined experimental and photochemical modeling study of the CH3 + CH3 reaction and its role in determining planetary CH3 abundances. In a discharge flow-mass spectrometer system, k was measured at T = 155 K and three pressures of He. The results in units of cm3 molecule-1 s-1 are k(0.6 Torr) = 6.82 ¿ 10-11, k(1.0 Torr) = 6.98 ¿ 10-11, and k(1.5 Torr) = 6.91 ¿ 10-11. Analytical expressions for k were derived that (1) are consistent with the present laboratory data at T = 155 K, our previous data at T = 202 K and 298 K, and those of other studies in He at T = 296--298 K and (2) have some theoretical basis to provide justification for extrapolation. The derived analytical expressions were then used in atmospheric photochemical models for both Saturn and Neptune. These model results reduced the disparity with observations of Saturn, but not with observations of Neptune. However, the disparity for Neptune is much smaller. The solution to the remaining excess CH3 prediction in the models relative to the ISO observations lies, to a large extent, elsewhere in the CH3 photochemistry or transport, not in the CH3 + CH3 rate.