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, 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. DOI: 10.1103/PhysRevB.81.172503 PACS number͑s͒: 74.62.Dh, 71.30.ϩh, 71.45.Lr, 74.25.Jb One of the most intriguing phenomena in the solid state is the occurrence of electronic instabilities toward broken symmetry states such as superconductivity ͑SC͒, density waves, charge and orbital order, or the Mott insulating state. When two or more instabilities are simultaneously at work, complex phase diagrams and unusual physical properties are found. Understanding such a coexistence or competition is therefore important. A related open issue is the emergence of SC from a normal state where the nature of the quasiparticles ͑QPs͒ is strongly modified by the interactions. Spectroscopic probes of the electronic states with momentum selectivity, namely, angle-resolved photoelectron spectroscopy ͑ARPES͒, can address these issues.Broken-symmetry phases are especially prominent in lowdimensional-quasi-one-dimensional ͑1D͒ and quasi-twodimensional ͑2D͒-materials.1 The 2D transition metal dichalcogenides ͑TMDs͒, in particular, exhibit a variety of charge-density wave ͑CDW͒ transitions.2 In their trigonal prismatic ͑2H͒ polytypes some of them also support SC, with critical temperatures as high as 7.2 K for NbSe 2 . ARPES has been used to identify in the band structure the favorable conditions for electronic instabilities. [3][4][5][6] According to the simplest Peierls scenario, the CDW is the result of a moderately strong electron-phonon ͑e-ph͒ interaction connecting electron and hole states across the well-nested Fermi surface ͑FS͒. SC is also a consequence of e-ph coupling, leading to the formation of Cooper pairs at the FS. Even if alternative scenarios been proposed which do not rely on nesting, 7,8 both CDW and SC tend to gap parts of the same FS and are generally considered to be competing.SC is usually not found in TMDs of the 1 T polytype, with TM ions in octahedral coordination, but it can be induced by doping or by external pressure. Recently, much interest has been raised by the observation that the balance between CDW and SC can be continuously tuned in the TMD TiSe 2 by a controlled intercalation of Cu atoms. 9 Here we consider the occurrence of SC in the isostructural TMD 1T-TaS 2 , which exhibits a unique sequence of CDW and Mott phases, as a result of the interplay of e-ph and Coulomb interactions.2 At room temperature ͑RT͒, the CDW is nearly commensurate ͑NC͒. It consists of a hexagonal array of domains separated by domain walls ͑discommensurations͒ where the CDW phase changes rapidly. The domain size and the CDW amplitude grow as temperature is reduced, ...