  Building on arXiv:1804.01998 we investigate the integrable structure of the
Wess-Zumino-Witten (WZW) model describing closed strings on $AdS_3\times
S^3\times T^4$. Using the recently-proposed integrable S matrix we show
analytically that all wrapping corrections cancel and that the theory has a
natural spin-chain interpretation. We construct the integrable spin chain and
discuss its relation with the WZW description. Finally we compute the
spin-chain spectrum in closed form and show that it matches the WZW prediction
on the nose.
