  We revisit the calculation of holographic correlators in $AdS_3$. We develop
new methods to evaluate exchange Witten diagrams, resolving some technical
difficulties that prevent a straightforward application of the methods used in
higher dimensions. We perform detailed calculations in the $AdS_3 \times S^3
\times K3$ background. We find strong evidence that four-point tree-level
correlators of KK modes of the tensor multiplets enjoy a hidden 6d conformal
symmetry. The correlators can all be packaged into a single generating
function, related to the 6d flat space superamplitude. This generalizes an
analogous structure found in $AdS_5 \times S^5$ supergravity.
