LS I +61 303 is an exceptionally rare example of a Be/X-ray binary that also exhibits MeV–TeV emission, making it one of only a handful of ”γ-ray binaries”. Here we present Hα spectra that show strong variability during the 26.5 day orbital period and over decadal time scales. The Hα line profile exhibits a dramatic emission burst shortly before apastron, observed as a redshifted shoulder in the line profile, as the compact source moves almost directly away from the observer. Here we investigate several possible origins for this red shoulder, including an accretion disk, tidal mass transfer stream, turbulent gas in the wake of the neutron star, and a compact pulsar wind nebula in the system.