  We study the problem $(-\Delta)^su=\lambda e^u$ in a bounded domain
$\Omega\subset\mathbb R^n$, where $\lambda$ is a positive parameter. More
precisely, we study the regularity of the extremal solution to this problem.
  Our main result yields the boundedness of the extremal solution in dimensions
$n\leq7$ for all $s\in(0,1)$ whenever $\Omega$ is, for every $i=1,...,n$,
convex in the $x_i$-direction and symmetric with respect to $\{x_i=0\}$. The
same holds if $n=8$ and $s\gtrsim0'28206...$, or if $n=9$ and
$s\gtrsim0'63237...$. These results are new even in the unit ball $\Omega=B_1$.
