  We study the commutant $L_{\widehat{\frak{sl}}_{2}}(n,0)^c$ of
$L_{\widehat{\frak{sl}}_{2}}(n,0)$ in the vertex operator algebra
$L_{\widehat{\frak{sl}}_{2}}(1,0)^{\otimes n}$, for $n\geq 2$. The main results
include a complete classification of all irreducible
$L_{\widehat{\frak{sl}}_{2}}(n,0)^c$-modules and a proof that
$L_{\widehat{\frak{sl}}_{2}}(n,0)^c$ is a rational vertex operator algebra. As
a consequence, every irreducible $L_{\widehat{\frak{sl}}_{2}}(n,0)^c$-module
arises from the coset construction as conjectured in \cite{LS}.
