The ability to cool atoms below the Doppler limit -- the minimum temperature
reachable by Doppler cooling -- has been essential to most experiments with
quantum degenerate gases, optical lattices and atomic fountains, among many
other applications. A broad set of new applications await ultracold molecules,
and the extension of laser cooling to molecules has begun. A molecular
magneto-optical trap has been demonstrated, where molecules approached the
Doppler limit. However, the sub-Doppler temperatures required for most
applications have not yet been reached. Here we cool molecules to 50 uK, well
below the Doppler limit, using a three-dimensional optical molasses. These
ultracold molecules could be loaded into optical tweezers to trap arbitrary
arrays for quantum simulation, launched into a molecular fountain for testing
fundamental physics, and used to study ultracold collisions and ultracold
chemistry.