Summary: We prove that the \(k\)th power \(G^{k}\) of a chordal graph \(G\) with maximum degree \(\Delta\) is \(O(\sqrt{k}\Delta^{(k+1)/2})\)-degenerate for even values of \(k\) and \(O(\Delta^{(k+1)/2})\)-degenerate for odd values. In particular, this bounds the chromatic number \(\chi(G^k)\) of the \(k\)th power of \(G\). The bound proven for odd values of \(k\) is the best possible. Another consequence is the bound \(\lambda_{p,q}(G)\leq \lfloor\frac{(\Delta+1)^{3/2}} {\sqrt{6}}\rfloor(2q-1)+\Delta(2p-1)\) on the least possible span \(\lambda_{p,q}(G)\) of an \(L(p,q)\)-labeling for chordal graphs \(G\) with maximum degree \(\Delta\). On the other hand, a construction of such graphs with \(\lambda_{p,q}(G)\geq\Omega(\Delta^{3/2}q+\Delta p)\) is found.