  We provide strong evidence that all tree-level 4-point holographic
correlators in AdS$_3 \times S^3$ are constrained by a hidden 6D conformal
symmetry. This property has been discovered in the AdS$_5 \times S^5$ context
and noticed in the tensor multiplet subsector of the AdS$_3 \times S^3$ theory.
Here we extend it to general AdS$_3 \times S^3$ correlators which contain also
the chiral primary operators of spin zero and one that sit in the gravity
multiplet. The key observation is that the 6D conformal primary field
associated with these operators is not a scalar but a self-dual $3$-form
primary. As an example, we focus on the correlators involving two fields in the
tensor multiplets and two in the gravity multiplet and show that all such
correlators are encoded in a conformal 6D correlator between two scalars and
two self-dual $3$-forms, which is determined by three functions of the cross
ratios. We fix these three functions by comparing with the results of the
simplest correlators derived from an explicit supergravity calculation.
