1T-TaS2 is a layered transition-metal dichalcogenide with a very rich phase diagram. At T=180 K it undergoes a metal to Mott insulator transition. Mott insulators usually display antiferromagnetic ordering in the insulating phase but 1T-TaS2 was never shown to order magnetically. In this paper we show that 1T-TaS2 has a large paramagnetic contribution to the magnetic susceptibility but it does not show any sign of magnetic ordering or freezing down to 20 mK, as probed by muon spin relaxation, possibly indicating a quantum spin liquid ground state. Although 1T-TaS2 exhibits a strong resistive behavior both in and out of plane at low temperatures we find a linear term in the heat capacity suggesting the existence of a Fermi surface, which has an anomalously strong magnetic field dependence.