In this paper we compute the 3-primary v₁-periodic homotopy groups of the exceptional Lie group E₇. This represents the next stage in the author's goal of calculating the v₁-periodic homotopy groups of all compact simple Lie groups (at least when localized at an odd prime). Most of the work goes into calculating the unstable Novikov spectral sequence of Ω E₇/Sp(2). Showing that this spectral sequence converges to the v₁-periodic homotopy groups in this case utilizes recent results of Bousfield and Bendersky-Thompson.