  In the AdS/CFT correspondence, single trace operators of large-$N$ gauge
theories at large spin $J$ can be described by classical spinning strings,
giving a geometric and classical description of their spectrum at strong
coupling. We observe that in AdS$_3$ these strings have significant
gravitational back-reaction at sufficiently large spin, since the gravitational
force does not decay at long distances. We construct solutions for folded
spinning strings coupled to gravity in AdS$_3$ and compute their spectrum,
corresponding to the leading Regge trajectory of Virasroro primary operators.
These solutions exist only below a maximal spin $J<J_\mathrm{max}$, and as
$J\to J_\mathrm{max}$ the solution approaches an extremal rotating BTZ black
hole.
