In this letter, we consider a power-constrained signal-to-noise ratio (SNR)-optimal collaborative beamformer (OCB) design in highly-scattered environments. We show that its weights depend on non-local CSI (NLCSI), thereby hampering its implementation in a distributed fashion. Exploiting the polychromatic (i.e., multi-ray) structure of scattered channels, we propose a novel distributed CB (DCB) design whose weights depends solely on local CSI (LCSI) and prove that it performs nearly as well as its NLCSI-based counterpart. Furthermore, we prove that the proposed LCSI-based DCB outperforms two other distributed-implementation benchmarks: the monochromatic (i.e., single-ray) DCB (M-DCB) whose design ignores the presence of scattering and the bichromatic (i.e., two-ray) DCB (B-DCB), which relies on an efficient polychromatic-channel approximation by two rays when the angular spread is relatively small.