We report measurements of the anisotropic upper critical field Hc2(T) for K2Cr3As3 single crystals up to 60 T and T>0.6K. Our results show that the upper critical field parallel to the Cr chains, H∥c2(T), exhibits a paramagnetically limited behavior, whereas the shape of the H⊥c2(T) curve (perpendicular to the Cr chains) has no evidence of paramagnetic effects. As a result, the curves H⊥c2(T) and H∥c2(T) cross at T≈4K, so that the anisotropy parameter γH(T)=H⊥c2/H∥c2(T) increases from γH(Tc)≈0.35 near Tc to γH(0)≈1.7 at 0.6 K. The paramagnetically limited behavior of H∥c2(T) is inconsistent with triplet superconductivity but suggests a form of singlet superconductivity with the electron spins locked onto the direction of Cr chains.