  We study Horowitz-Polchinski string stars in pure AdS$_3$ near the Hagedorn
temperature using the technique of worldsheet conformal perturbation theory.
Since the worldsheet CFT for pure AdS$_3$ is known exactly, our methodology
provides a systematic way to construct Horowitz-Polchinski backgrounds to all
orders in $\alpha'$. We explicitly construct the leading string star equations
in a double expansion in temperature and WZW level $k$ which we then solve
numerically.
