Olfactory systems must detect and discriminate an enormous diversity of chemicals in the environment. To contend with this challenge, diverse species have converged on a common strategy in which odorant identity is encoded through the combinatorial activation of large families of olfactory receptors (ORs), thus allowing a finite number of receptors to detect an almost infinite chemical world. Although most individual ORs are sensitive to a variety of odorants, the structural basis for such flexible chemical recognition remains unknown. Here, we combine cryo-electron microscopy with functional studies of receptor tuning to gain insight into the structural and mechanistic basis of promiscuous odorant recognition. We show that OR5 from the jumping bristletail, Machilis hrabei, assembles as a homo-tetrameric odorant-gated ion channel with broad chemical tuning. We elucidated the structure of OR5 in multiple gating states, alone and in complex with two of its agonists—the odorant eugenol and the insect repellent DEET. Both ligands bind to a common binding site located in the transmembrane region of each subunit, composed of a simple geometric arrangement of aromatic and hydrophobic residues. We reveal that binding is mediated by hydrophobic, non-directional interactions with residues distributed throughout the binding pocket, enabling the flexible recognition of structurally distinct odorants. Mutation of individual residues lining the binding pocket predictably altered OR5’s sensitivity to eugenol and DEET and broadly reconfigured the receptor’s tuning, supporting a model in which diverse odorants share the same structural determinants for binding. Together, these studies provide structural insight into odorant detection, shedding light onto the molecular recognition mechanisms that ultimately endow the olfactory system with its immense discriminatory capacity.