H-alpha, R, and I band CCD images of the "posteruptive" irregular galaxy NGC 1569 are presented. The discovery of two arclike structures of diffuse H-alpha emission located more than 1 kpc beyond the star-forming bar is reported. These features are used to estimate an age for the near-nuclear starburst that created them along with other filamentary and armlike structures previously seen in H-alpha photographs. Considerations of likely outflow geometries and kinematics lead to an estimated age range of 10-60 Myr, in rough accord with the 10-20 Myr age that Israel and de Bruyn derive based on considerations of synchrotron losses in the nonthermal radio spectrum. The gravitational and kinematic energies associated with the H-alpha arcs are estimated to be orders of magnitude higher than can be provided by a single supernova explosion. Coherent outbursts involving thousands of supernovae each could explain the diffuse H-alpha features without exceeding the starbirth rate inferred from the total H-alpha luminosity of the galaxy. Comparisons between the line and continuum imagery show the inner bar to be populated with H II regions of high H-alpha equivalent width and blue color. These regions are located on opposite sides of the brightest continuum emission which, in turn, is offset from the dynamical nucleus as defined by the outer B and V isophotes. A starburst history incorporating these observations is proposed and discussed.