Between 1994 July and 1997 February we monitored the optical spectrum of RX J0019.8]2156. This supersoft X-ray source is one of only two accreting white dwarfs in the Galaxy that are thought to be burning hydrogen on their surface as a consequence of a high rate of mass transfer from a binary companion. Accurate orbital ephemerides are derived from radial velocity measurements for the white dwarf, which are obtained from strong He II emission lines with a stable velocity semiamplitude of K \ 71.2^3.6 km s~1. We report the discovery of transient, low-velocity, bipolar jets. These jets are represented by redshifted-blueshifted pairs of emission lines from H and He II with an outÑow velocity of v cos (i) D 815 km s~1, where i is the binary inclination angle. When present, the jet lines seen in Ha also exhibit an orbital modulation of 71 km s~1, which strengthens the interpretation that this is the orbital velocity of the white dwarf and also indicates that the jets are oriented nearly perpendicular to the orbital plane. On most occasions, the H emission line proÐles are further altered by P Cygni absorption e †ects, and the strength of this absorption is also dependent on binary phase. We show that the jets and the P Cygni features have very di †erent temporal characteristics and binary phase dependence ; thus, we conclude that the outÑowing material and the absorbing wind must have essentially di †erent geometries. Finally, the measured mass function is combined with binary evolution models to suggest a limit on the inclination angle, i \ 40¡. A particular model invoked to explain a high rate of mass transfer requires 16¡ \ i \ 25¡. However, at such small inclination it is difficult to explain the large amplitude of the orbital light curve (D0.5 mag). Alternatively, the results could signify substantial vertical structure in the accretions disks of supersoft X-ray sources. By contrast, a simple model Ðt to the jet outÑow lines indicates an orbital inclination angle of 35¡ \ i \ 60¡.