  We report the in-plane resistivity and magnetic susceptibility of the layered
cobalt oxide Na$_{0.35}$CoO$_{2}{\cdot}1.3$H$_{2}$O single crystal. The
temperature dependence of the resistivity shows metallic behavior from room
temperature to the superconducting transition temperature $T_{c}$ of 4.5 K.
Sharp resistive transition, zero resistivity and almost perfect superconducting
volume fraction below $T_{c}$ indicate the good quality and the bulk
superconductivity of the single crystal. The upper critical field $H_{c2}$ and
the coherence length $\xi$ are obtained from the resistive transitions in
magnetic field parallel to the c-axis and the $ab$-plane. The anisotropy of
$\xi$, $\xi_{ab} / \xi_{c} =$ 12 nm/1.3 nm $\simeq$ 9.2, suggests that this
material is considered to be an anisotropic three dimensional superconductor.
In the field parallel to the $ab$-plane, $H_{c2}$ seems to be suppressed to the
value of Pauli paramagnetic limit. It may indicate the spin singlet
superconductivity in the cobalt oxide.
