  At $n=3/4$ filling of the moir\'e flat band, transition metal dichalcogenide
moir\'e bilayers will develop kagome charge order. We derive an effective spin
model for the resulting localized spins and find that its further neighbor spin
interactions can be much less suppressed than the corresponding electron
hopping strength. Using density matrix renormalization group simulations, we
study its phase diagram and, for realistic model parameters relevant for
WSe$_2$/WS$_2$, we show that this material can realize the exotic chiral spin
liquid phase and the highly debated kagome spin liquid. Our work thus
demonstrates that the frustration and strong interactions present in TMD
heterobilayers provide an exciting platform to study spin liquid physics.
