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Binary interactions have been proposed to explain a variety of circumstellar structures seen around evolved stars, including asymptotic giant branch (AGB) stars and planetary nebulae. Studies resolving the circumstellar envelopes of AGB stars have revealed spirals, disks and bipolar outflows, with shaping attributed to interactions with a companion. Here we use a combined chemical and dynamical analysis to reveal a highly eccentric and long-period orbit for W Aquilae, a binary system containing an AGB star and a main-sequence companion. Our results are based on anisotropic SiN emission, the detections of irregular NS and SiC emission towards the S-type star, and density structures observed in the CO emission. These features are all interpreted as having formed during periastron interactions. Our astrochemistry-based method can yield stringent constraints on the orbital parameters of long-period binaries containing AGB stars, and will be applicable to other systems. When stars like our Sun die, they expel their outer layers in a dramatic stellar wind. This study of an unusual chemical signature in one particular stellar wind reveals that the signature is due to the presence of a binary system whose components had a close approach around 200 years ago.