  We report the first measurements of the anisotropic upper critical field
$H_{c2}(T)$ for K$_{2}$Cr$_{3}$As$_{3}$ single crystals up to 60 T and $T >
0.6$ K. Our results show that the upper critical field parallel to the Cr
chains, $H_{c2}^\parallel (T)$, exhibits a paramagnetically-limited behavior,
whereas the shape of the $H_{c2}^\perp (T)$ curve (perpendicular to the Cr
chains) has no evidence of paramagnetic effects. As a result, the curves
$H_{c2}^\perp (T)$ and $H_{c2}^\parallel(T)$ cross at $T\approx 4$ K, so that
the anisotropy parameter $\gamma_H(T)=H_{c2}^\perp/H_{c2}^\parallel (T)$
increases from $\gamma_H(T_c)\approx 0.35$ near $T_c$ to $\gamma_H(0)\approx
1.7$ at 0.6 K. This 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.
