We have obtained emission-line and continuum images of the young planetary nebula MyCn 18 with the Wide Field Planetary Camera 2 on the Hubble Space Telescope (HST). Although from the ground MyCn 18 appeared to have a triple-ring structure similar to SN 1987A, the HST images show that MyCn 18 has an overall hourglass shape. A series of arcs appear to be etched on the walls of the hourglass near its rims. In the complex central region of the nebula we find a small, inner hourglass structure and two rings. Ring 1 is a bright elliptical ring, and ring 2 a smaller, higher excitation ring. The outer and inner hourglass, and ring 1 and ring 2, all have different centers, and none are coincident with the central star. The hourglass shape of the main nebula is consistent with the predictions of the generalized interacting-winds hypothesis for planetary nebula formation. However, the complex inner nebular structure of MyCn 18 and the offset of the central star from the center of the nebula remain a mystery. We discuss several mechanisms for producing the offset of the central star. Although none are found to be completely satisfactory, those involving a binary central star probably offer the best hope of successful explanation.