We have used the WFPC2 camera aboard the Hubble Space Telescope to obtain images of the Seyfert galaxy NGC 3516 in the [O III] lambda 5007 and [N II] lambda lambda 6548, 6583 + H alpha emission lines as well as in their adjacent continua. The emission-line images reveal a close morphological association between an arclike structure 1".7 north of the nucleus and radio emission. The line-emitting gas to the southwest of the nucleus contains dust that obscures the light of the galaxy bulge, suggesting that the gas lies on the near side of the galaxy disk. In contrast, the gas to the northeast does not obscure the bulge light and its line emission is partially obscured by dust lanes running approximately parallel to the disk major axis just to the north of the nucleus. The gas to the northeast of the nucleus thus seems to lie on the far side of the disk. The dust lanes strongly suggest that the northwest side of the galaxy disk is the near side. The consequences of this geometry for the kinematics of the ionized gas are discussed.