We present global VLBI observations of the first-excited state OH masers in the massive star-forming region Onsala 1 (ON 1). The 29 masers detected are nearly all from the 6035 MHz transition, and nearly all are identifiable as Zeeman pair components. The 6030 and 6035 MHz masers are coincident with previously published positions of ground-state masers to within a few milliarcseconds, and the magnetic fields deduced from Zeeman splitting are comparable. The 6.0 GHz masers in ON 1 are always found in close spatial association with 1665 MHz OH masers, in contrast to the situation in the massive star-forming region W3(OH), suggesting that extreme high density OH maser sites (excited-state masers with no accompanying ground-state maser, as seen in W3(OH)) are absent from ON 1. The large magnetic field strength among the northern, blueshifted masers is confirmed. The northern masers may trace an outflow or be associated with an exciting source separate from the other masers, or the relative velocities of the northern and southern masers may be indicative of expansion and rotation. High angular resolution observations of nonmasing material will be required to understand the complex maser distribution in ON 1.