  The clique vector $\mathfrak{c}(G)$ of a graph $G$ is the sequence $(c_1,
c_2, \ldots,c_d)$ in $\mathbb{N}^d$, where $c_i$ is the number of cliques in
$G$ with $i$ vertices and $d$ is the largest cardinality of a clique in $G$. In
this note, we use tools from commutative algebra to characterize all possible
clique vectors of $k$-connected chordal graphs.
