Summary: We carry out an exact worldsheet computation of tree level three-point correlators of chiral operators in string theory on \(\text{AdS}_3\times S^3\times T^4\) with NS-NS flux. We present a simple representation for the string chiral operators in the coordinate basis of the dual boundary CFT. Striking cancelations occur between the three-point functions of the \(H_3^+\) and the SU(2) WZW models which result in a simple factorized form for the final correlators. We show, by fixing a single free parameter in the \(H_3^+\) WZW model, that the fusion rules and the structure constants of the \(N=2\) chiral ring in the bulk are in precise agreement with earlier computations in the boundary CFT of the symmetric product of \(T^4\) at the orbifold point in the large \(N\) limit.