We build ab initio three-body potential energy surfaces for clusters of the type CO-(pH(2))(n). The configuration space of the trimers (H-2)(3) and CO-(H-2)(2) is sampled with coupled-cluster calculations and the three-body contributions to the nine-dimensional potential energy surface in the van der Waals well are fitted with a neural-network based method of Manzhos and Carrington [ 26] using dimensionality reduction. The resulting three-body corrections can be used with high-quality pairwise-additive potentials for (H-2)(2) and CO-H-2 available in the literature to build a potential energy surface for CO molecules trapped in solid para-hydrogen. (C) 2010 Elsevier B. V. All rights reserved.