Exciton condensates (EC) are macroscopic coherent states arising from condensation of electron-hole pairs. Bilayer heterostructures, consisting of two-dimensional electron and hole layers separated by a tunnel barrier, provide a versatile platform to realize and study EC. The tunnel barrier suppresses recombination yielding long-lived excitons. However, this separation also reduces interlayer Coulomb interactions, limiting the exciton binding strength. Here, we report the observation of EC in naturally occurring 2H-stacked bilayer WSe$_2$. In this system, the intrinsic spin-valley structure suppresses interlayer tunneling even when the separation is reduced to the atomic limit, providing access to a previously unattainable regime of strong ...