  The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is an exotic
superconducting phase formed by Cooper pairs with finite center-of-mass
momentum $q$. On theoretical grounds, the superconducting order parameter in
the FFLO state is spatially modulated along the $q$ vector, and the emergence
of an associated anisotropy is expected at the phase transition from the
Abrikosov state to the FFLO state. Here, we report the results of
high-resolution magnetostriction measurements for a single crystal of
CeCoIn$_5$ around $B \parallel c$. We find two anomalies in the
magnetostriction along the $c$ axis, parallel to the magnetic-field
orientation. In sharp contrast, this $B_{\rm K}$ anomaly disappears in the
magnetostriction along the $a$-axis direction, perpendicular to the
magnetic-field orientation. To explain this uniaxial expansion, we suggest a
possibility that the FFLO transition occurs slightly below the upper critical
field, and the FFLO modulation vector parallel to the applied magnetic field
gives rise to the anisotropic response.
