Biased agonists, which selectively stimulate certain signaling pathways controlled by a G protein-coupled receptor (GPCR), hold great promise as drugs that maximize efficacy while minimizing dangerous side effects. Biased agonists of the μ-opioid receptor (μOR) are of particular interest as a means to achieve analgesia through G protein signaling without dose-limiting side effects such as respiratory depression and constipation. Rational structure-based design of biased agonists remains highly challenging, however, because the ligand-mediated interactions that are key to activation of each signaling pathway remain unclear. We identify several compounds for which the R- and S-enantiomers have distinct bias profiles at the μOR. These compounds serve as excellent comparative tools to study bias because the identical physicochemical properties of enantiomer pairs ensure that differences in bias profiles are due to differences in interactions with the μOR binding pocket. Atomic-level simulations of compounds at μOR indicate that R- and S-enantiomers adopt different poses that form distinct interactions with the binding pocket. A handful of specific interactions with highly conserved binding pocket residues appear to be responsible for substantial differences in arrestin recruitment between enantiomers. Our results offer guidance for rational design of biased agonists at μOR and possibly at related GPCRs.