  We propose a novel Sisyphus cooling scheme for atoms confined in a far off
resonance optical dipole trap. Utilizing the differential trap-induced AC Stark
shift, two electronic levels of the atom are resonantly coupled by a cooling
laser preferentially near the trap bottom. After absorption of a cooling
photon, the atom loses energy by climbing the steeper potential, and then
spontaneously decays preferentially away from the trap bottom. The proposed
method is particularly suited to cooling alkaline-earth-like atoms where
two-level systems with narrow electronic transitions are present. Numerical
simulations for the cases of $^{88}$Sr and $^{174}$Yb demonstrate the expected
recoil and Doppler temperature limits. The method requires a relatively small
number of scattered photons and can potentially lead to phase space densities
approaching quantum degeneracy in sub-second timescales.
