Measurements of temperature-dependent in-plane resistivity ρ(T) were used to determine the upper critical field and its anisotropy in high-quality single crystals of the stoichiometric iron arsenide superconductor KFe2As2. The crystals were characterized by the residual resistivity ratio ρ(300 K)/ρ(0) up to 3000 and the resistive transition midpoint temperature Tc=3.8 K, significantly higher than in previous studies on the same material. We find increased Hc2(T) for both directions of the magnetic field, which scale with the increased Tc. This unusual linear Hc2(Tc) scaling is not expected for an orbital-limiting mechanism of the upper critical field in clean materials.