Coexistence of reversible polar distortions and metallicity leading to a ferroelectric metal, first suggested by Anderson and Blount in 1965, has so far remained elusive. Electrically switchable intrinsic electric polarization, together with the direct observation of ferroelectric domains, has not yet been realized in a bulk crystalline metal, although incomplete screening by mobile conduction charges should, in principle, be possible. Here, we provide evidence that native metallicity and ferroelectricity coexist in bulk crystalline van der Waals WTe2 by means of electrical transport, nanoscale piezoresponse measurements, and first-principles calculations. We show that, despite being a Weyl semimetal, WTe2 has switchable spontaneous polarization and a natural ferroelectric domain structure at room temperature. This new class of materials has tantalizing potential for functional nanoelectronics applications.