  The Stieltjes constants $\gamma_n$ appear in the coefficients in the Laurent
expansion of the Riemann zeta function $\zeta(s)$ about the simple pole $s=1$.
We present an asymptotic expansion for $\gamma_n$ as $n\rightarrow \infty$
based on the approach described by Knessel and Coffey [Math. Comput. {\bf 80}
(2011) 379--386]. A truncated form of this expansion with explicit coefficients
is also given. Numerical results are presented that illustrate the accuracy
achievable with our expansion.
