A method to construct an accurate potential energy surface (PES) by interpolation for a three-body reaction which is suitable for quantum dynamics studies is presented using Cl+H-2--> HCl+H as an example. Use of the exponential coordinates led to a significant improvement. Dynamics results, both classical and quantal, on the LEPS and LEPS-interpolated PESs were nearly indistinguishable. An accurate analytic PES can be constructed with the ab initio results also, as manifested with the PES contours.