The planetary nebula TS 01 (also called PN G 135.9+55.9 or SBS 1150+599A) with its record-holding low oxygen abundance and its double degenerate close binary core (period 3.9 h) is an exceptional object located in the Galactic halo. We have secured observational data in a complete wavelength range to pin down the abundances of half a dozen elements in the nebula. The abundances are obtained via detailed photoionization modelling which takes into account all the observational constraints (including geometry and aperture effects) using the pseudo-3D photoionization code Cloudy_3D. The spectral energy distribution of the ionizing radiation is taken from appropriate model atmospheres. Incidentally we find from the new observational constraints that both stellar components contribute to the ionization: the “cool” one provides the bulk of hydrogen ionization, while the “hot” one is responsible for the presence of the most highly charged ions, which explains why previous attempts to model the nebula experienced difficulties. The nebular abundances of C, N, O, and Ne are found to be 1/3.5, 1/4.2, 1/70, and 1/11 of the solar value respectively, with uncertainties of a factor 2. Thus the extreme O deficiency of this object is confirmed. The abundances of S and Ar are less than 1/30 of solar. The abundance of He relative to H is 0.089 ± 0.009. Standard models of stellar evolution and nucleosynthesis cannot explain the abundance pattern observed in the nebula. To obtain an extreme oxygen deficiency in a star whose progenitor has an initial mass of about 1 M&sun; requires an additional mixing process, which can be induced by stellar rotation and/or by the presence of the close companion. We have computed a stellar model with an initial mass of 1 M&sun;, appropriate metallicity, and initial rotation of 100 km s-1, and find that rotation greatly improves the agreement between the predicted and observed abundances. Based on observations obtained at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council of Canada, the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawaii.Based on observations 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.Based on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under NASA contract 1407.