We grew single crystals of the recently discovered heavy fermion superconductor UTe2, and measured the resistivity, specific heat and magnetoresistance. Superconductivity (SC) was clearly detected at Tsc = 1.65 K as sharp drop of the resistivity in a high quality sample of RRR = 35. The specific heat shows a large jump at Tsc indicating strong coupling. The large Sommerfeld coefficient, γ = 117 mJ K−2 mol−1 extrapolated in the normal state and the temperature dependence of C=T below Tsc are the signature of unconventional SC. The discrepancy in the entropy balance at Tsc between SC and normal states points out that hidden features must occur. Surprisingly, a large residual value of the Sommerfeld coefficient seems quite robust (γ0=γ ∼ 0.5). The large upper critical field Hc2 along the three principal axes favors spin-triplet SC. For H ∥ b-axis, our experiments do not reproduce the huge upturn of Hc2 reported previously. This discrepancy may reflect that Hc2 is very sensitive to the sample quality. A new perspective in UTe2 is the proximity of a Kondo semiconducting phase predicted by the LDA band structure calculations.