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 in order to pin down the abundances of half a dozen elements in the nebula. The abundances are obtained via detailed photoionization modelling taking 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. Both stellar components contribute to the ionization: the ``cool'' one provides the bulk of hydrogen ionization, and 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 respectively, 1/3.5, 1/4.2, 1/70, and 1/11 of the Solar value, 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. 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 msun 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 initial mass of 1 msun, appropriate metallicity, and initial rotation of 100 kms, and find that rotation greatly improves the agreement between the predicted and observed abundances.