Nodal line semimetals are characterized by nontrivial bulk-band crossings, giving rise to almost flat drumheadlike surface states (DSS), which provide an attractive playground where interaction can induce symmetry-broken states and potential emergent phases. Here, we show that electronic interaction drives a Stoner ferromagnetic instability in the DSS while the bulk remains nonmagnetic, which together with spin-orbit coupling drive the surface states into a 2D Chern insulator. We show that each piece of DSS carries a half-integer topological charge, which for systems containing two pieces of DSS yield a net Chern number C=-1. We show that this phenomenology is robust against chiral-symmetry breaking, which gives a finite dispersion to the DSS. Our results show that nodal line semimetals are a promising platform to implement surface Chern insulators and dissipationless electron transport by exploiting enhanced interaction effects of the DSS.