  When a Mott metal-insulator transition is inhibited by a small amount of
disorder in the layered dichalcogenide 1T-TaS$_2$, an inhomogeneous
superconducting state arises below T=2.1 K, and coexists with a
nearly-commensurate charge-density-wave. By angle-resolved photoelectron
spectroscopy (ARPES) we show that it emerges from a bad metal state with
strongly damped quasiparticles. Superconductivity is almost entirely suppressed
by an external magnetic field of 0.1 T.
