The magnetoresistance and magnetic torque of FeS are measured in magnetic fields B of up to 18 T down to a temperature of 0.03 K. The superconducting transition temperature is found to be Tc = 4.1 K, and the anisotropy ratio of the upper critical field Bc2 at Tc is estimated from the initial slopes to be Γ(Tc) = 6.9. Bc2(0) is estimated to be 2.2 and 0.36 T for B ab and c, respectively. Quantum oscillations are observed in both the resistance and torque. Two frequencies F = 0.15 and 0.20 kT are resolved and assigned to a quasi-two-dimensional Fermi surface cylinder. The carrier density and Sommerfeld coefficient associated with this cylinder are estimated to be 5.8 × 10−3 carriers/Fe and 0.48 mJ/(K 2 mol), respectively. Other Fermi surface pockets still remain to be found. Band-structure calculations are performed and compared to the experimental results.