  In this work we study the crystal symmetry fractionalization in chiral spin
liquids with the chiral-semion topological order. We show that if such a chiral
spin liquid is realized in a two-dimensional lattice model with odd number of
spin-$\frac12$ per unit cell and the state preserves spin rotation symmetry and
translation symmetries, the semion excitation must carry both half-integer spin
and fractional crystal quantum numbers. As a result, only a unique symmetry
enriched topological phase can be realized in chiral spin liquids in a
spin-$\frac12$ kagome lattice model. These fractional symmetry quantum numbers
are confirmed numerically using ground state wave functions obtained with the
density matrix renormalization group method.
