Mapping genetic interactions (GIs) by simultaneously perturbing pairs of genes is a powerful tool for understanding complex biological phenomena. Here we describe an experimental platform for generating quantitative GI maps in mammalian cells using a combinatorial RNA interference strategy. We performed ∼11,000 pairwise knockdowns in mouse fibroblasts, focusing on 130 factors involved in chromatin regulation to create a GI map. Comparison of the GI and protein-protein interaction (PPI) data revealed that pairs of genes exhibiting positive GIs and/or similar genetic profiles were predictive of the corresponding proteins being physically associated. The mammalian GI map identified pathways and complexes but also resolved functionally distinct submodules within larger protein complexes. By integrating GI and PPI data, we created a functional map of chromatin complexes in mouse fibroblasts, revealing that the PAF complex is a central player in the mammalian chromatin landscape.