  We perform the first lattice QCD calculation of the form factors governing
the $\Xi_{c}\to \Xi \ell^+\nu_{\ell}$ using the 2+1 clover fermion ensembles
with two lattice spacings, $a=(0.108{\rm fm},0.080{\rm fm})$. After the
continuum extrapolation, partial decay widths are calculated. Using the
$|V_{cs}|$ from global fit and the $\Xi_{c}$ lifetimes, we predict branching
fractions as ${\cal B}(\Xi_{c}^0\to \Xi^- e^+ \nu_{e})=2.38(0.30)(0.33)\% $,
${\cal B}(\Xi_{c}^0\to \Xi^- \mu^+ \nu_{\mu})=2.29(0.29)(0.31)\% $, ${\cal
B}(\Xi_{c}^+\to \Xi^0 e^+ \nu_{e})= 7.18(0.90)(0.98)\%$, and ${\cal
B}(\Xi_{c}^+\to \Xi^0 \mu^+ \nu_{\mu})= 6.91(0.87)(0.93)\%$, with the two kinds
of uncertainties coming from statistical fluctuations in form factors and
$\Xi_c$ lifetimes, and systematic ones from continuum extrapolation and
renormalization, respectively. Combing the experimental measurement by Belle,
we determine the CKM matrix element as $|V_{cs}|=0.834(0.074)(0.127)$, where
the two uncertainties come from theory and data.
