  Given $t\geq 2$ and $0\leq k\leq t$, we prove that the number of labelled
$k$-connected chordal graphs with $n$ vertices and tree-width at most $t$ is
asymptotically $c n^{-5/2} \gamma^n n!$, as $n\to\infty$, for some constants
$c,\gamma >0$ depending on $t$ and $k$. Additionally, we show that the number
of $i$-cliques ($2\leq i\leq t$) in a uniform random $k$-connected chordal
graph with tree-width at most $t$ is normally distributed as $n\to\infty$.
  The asymptotic enumeration of graphs of tree-width at most $t$ is wide open
for $t\geq 3$. To the best of our knowledge, this is the first non-trivial
class of graphs with bounded tree-width where the asymptotic counting problem
is solved. Our starting point is the work of Wormald [Counting Labelled Chordal
Graphs, Graphs and Combinatorics (1985)], were an algorithm is developed to
obtain the exact number of labelled chordal graphs on $n$ vertices.
