Iota Orionis is a massive binary with a very eccentric orbit, which brings the stars into close proximity at periastron. The resulting tidal deformation of the primary star is expected to create enhanced mass loss and stimulate stellar oscillations at each periastron. We present the results of a search for these effects in high S/N spectra of the H and He I λ6678 profiles of ι Ori obtained over 5.5 hr during a single periastron passage. We fit the He I λ6678 data using previously determined profiles for both components and using the orbital solution of Stickland et al. (1987) to establish that periastron occurred at HJD 2,45007280±0.03. Measurements of the projected rotational velocities indicate that both stars rotate more slowly than the orbit at periastron. There is weak, residual Hα emission that moves with the primary's orbital motion and that may be associated with the development of an enhanced, focused wind at periastron. However, the He I λ6678 line of the primary star is nearly constant in shape over this interval, and we find no evidence for tidally induced oscillations.