  We predict that the gapless $U(1)$ Dirac spin liquid naturally emerges in a
two-dimensional array of quantum dipoles. In particular, we demonstrate that
the dipolar XY model$\unicode{x2014}$realized in both Rydberg atom arrays and
ultracold polar molecules$\unicode{x2014}$hosts a quantum spin liquid ground
state on the kagome lattice. Large-scale density matrix renormalization group
calculations indicate that this spin liquid exhibits signatures of gapless,
linearly-dispersing spinons, consistent with the $U(1)$ Dirac spin liquid. We
identify a route to adiabatic preparation via staggered on-site fields and
demonstrate that this approach can prepare cold spin liquids within
experimentally realistic time-scales. Finally, we propose a number of novel
signatures of the Dirac spin liquid tailored to near-term quantum simulators,
including termination-dependent edge modes and the Friedel response to a local
perturbation.
