  The temperature dependence of the upper critical field ($H_{c2}$) in RbCr$%
_{3}$As$_{3}$ single crystals ($T_{c}\approx $ 7.3 K) has been determined by
means of magnetoresistance measurements with temperature down to 0.35 K in
static magnetic fields up to 38 T. The magnetic field was applied both for
directions parallel ($H\parallel c $, $H_{c2}^{\parallel c}$) and perpendicular
($H\perp c$, $H_{c2}^{\perp c}$) to the Cr chains. The curves
$H_{c2}^{\parallel c}(T)$ and $H_{c2}^{\perp c}(T)$ cross at $\sim $ 5.5 K. As
a result, the anisotropy parameter $\gamma (T)=H_{c2}^{\perp
c}/H_{c2}^{\parallel c}(T)$ increases from 0.5 near $T_{c}$ to 1.6 at low
temperature. Fitting with the Werthamer-Helfand-Hohenberg (WHH) model yields
zero-temperature critical fields of $\mu_0H_{c2}^{\parallel c}(0)\approx $ 27.2
T and $\mu_0H_{c2}^{\perp c}(0)\approx $ 43.4 T, both exceeding the BCS
weak-coupling Pauli limit $\mu_0H_{p}=1.84T_{c}=13.4$ T. The results indicate
that the paramagnetic pair breaking effect is strong for $H \parallel c$ but
absent for $H \perp c$, which was further confirmed by the angle dependent
magnetoresistance and $H_{c2}$ measurements.
