  We report measurements of the coefficient of linear thermal expansion,
$\alpha (T)$, of the superconducting ferromagnet UCoGe. The data taken on a
single-crystalline sample along the orthorhombic crystal axes reveal a
pronounced anisotropy, with the largest length changes along the $b$ axis. The
large values of the step sizes $\Delta \alpha$ at the magnetic and
superconducting phase transitions provide solid evidence for bulk magnetism and
superconductivity. Specific-heat measurements corroborate bulk
superconductivity. Thermal-expansion measurements in magnetic fields $B
\parallel a,b$ show $\Delta \alpha$ at $T_C$ grows rapidly, which indicates the
character of the ferromagnetic transition becomes first-order-like.
