We present a fully differential next-to-next-to-leading order calculation of charm-quark production in charged-current deep-inelastic scattering, with full charm-quark mass dependence. The next-to-next-toleading order corrections in perturbative quantum chromodynamics are found to be comparable in size to the next-to-leading order corrections in certain kinematic regions. We compare our predictions with data on dimuon production in (anti)neutrino scattering from a heavy nucleus. Our results can be used to improve the extraction of the parton distribution function of a strange quark in the nucleon. DOI: 10.1103/PhysRevLett.116.212002 Introduction.-Charm-quark (c) production in deepinelastic scattering (DIS) of a neutrino from a heavy nucleus provides direct access to the strange-quark (s) content of the nucleon. At lowest order, the relevant partonic process is neutrino interaction with a strange quark, νs → cl, mediated by weak vector boson W exchange. Another source of constraints is charm-quark production in association with a W boson at hadron colliders, gs → cW. The DIS data determine parton distribution functions (PDFs) in the nucleon whose detailed understanding is vital for precise predictions at the Large Hadron Collider (LHC). The strangequark PDF can play an important role in LHC phenomenology, contributing, for example, to the total PDF uncertainty in W or Z boson production [1,2], and to systematic uncertainties in precise measurements of the W boson mass and weak-mixing angle [3][4][5]. It is estimated that the PDF uncertainty of the strange quark alone could lead to an uncertainty of about 10 MeV on the W boson mass measurement at the LHC [6]. From the theoretical point of view, it is important to test whether the strange PDFs are suppressed compared to those of other light sea quarks, related to the larger mass of the strange quark, as suggested by various models [7][8][9], and to establish whether there is a difference between the strange-and antistrange-quark PDFs.In this Letter, we report on a complete calculation at next-to-next-to-leading order (NNLO) in pertubative quantum chromodynamics (QCD) of charm-quark production in DIS of a neutrino from a nucleon. Our calculation is based on a phase-space slicing method and uses a fully differential Monte Carlo integration. It maintains the exact mass dependence and all kinematic information at the parton level. The NNLO corrections can change the cross sections by up to 10%, depending on the kinematic region considered. Our results show that the next-to-leading-order (NLO) predictions underestimate the perturbative uncertainties