Coulomb drag is a frictional coupling between electric currents flowing in spatially separated conducting layers. It is caused by interlayer electron–electron interactions. Previously, only the regime of weak (ddouble greater thanl) to intermediate (d~l) coupling could be studied experimentally, where dis the interlayer separation and l is the characteristic distance between charge carriers. Here we use graphene–boron-nitride heterostructures with d down to 1 nm to probe Coulomb drag in the limit dless doublel such that the two Dirac liquids effectively nest within the same plane, but can still be tuned and measured independently. The strongly interacting regime reveals many unexpected features. In particular, although drag vanishes because of electron–hole symmetry when either layer is neutral, we often find drag strongest when both layers are neutral. Under this circumstance, drag is positive in zero magnetic field but changes its sign and rapidly grows in strength with field. The drag remains strong at room temperature. The broken electron–hole symmetry is attributed to mutual polarization of closely spaced interacting layers.