  The in-plane thermal conductivity $\kappa$ of the iron selenide
superconductor FeSe$_x$ ($T_c$ = 8.8 K) were measured down to 120 mK and up to
14.5 T ($\simeq 3/4 H_{c2}$). In zero field, the residual linear term
$\kappa_0/T$ at $ T \to 0$ is only about 16 $\mu$W K$^{-2}$ cm$^{-1}$, less
than 4% of its normal state value. Such a small $\kappa_0/T$ does not support
the existence of nodes in the superconducting gap. More importantly, the field
dependence of $\kappa_0/T$ in FeSe$_x$ is very similar to that in NbSe$_2$, a
typical multi-gap s-wave superconductor. We consider our data as strong
evidence for multi-gap nodeless superconductivity in FeSe$_x$. This kind of
superconducting gap structure may be generic for all Fe-based superconductors.
