Hubble Space Telescope (HST) and ground-based [O II] and [N II] images obtained in the period 1996-1999 reveal a complex, ionized optical nebula around the symbiotic binary CH Cyg extending out to 18" or 5000 AU from the central stars. The observed velocity range of the nebula, derived from long-slit echelle spectra, is 130 km s-1. In spite of its complex appearance, the velocity data show that the basic morphology of the inner regions of the optical nebula is that of a bipolar outflow extending nearly along the plane of the sky out to some 2000 AU from the center. Even if the extension of this bipolar outflow and its position angle are consistent with those of the radio jet produced in 1984 (extrapolated to the time of our optical imagery), no obvious optical counterpart is visible to the original, dense radio bullets ejected by the system. We speculate that the optical bipolar outflow might be the remnant of the interaction of the bullets with a relatively dense circumstellar medium. Based on observations obtained at the 4.2 m William Herschel Telescope and 2.6 m Nordic Optical Telescope operated on the island of La Palma by the Isaac Newton Group and the Nordic Optical Telescope Scientific Association (NOTSA), respectively, at the Spanish Observatorio del Roque de Los Muchachos of the Instituto de Astrofísica de Canarias, and with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.