Abstract: Following a strategy developed by Athreya and Cheung, we compute the gap distribution of the slopes of saddle connections on the translation surface associated to the regular octagon by translating the problem to a question about return times of the horocycle flow to an appropriate Poincare Section. This same strategy was used by Athreya, Chaika, and Lelievre to compute the gap distribution on the Golden L. The octagon is the first example of this type of computation where the Veech group has two cusps.