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27 pags., 9 figs., 10 tabs., 3 apps., We present the first unbiased molecular line survey toward an extragalactic source, namely the nuclear region of the starburst galaxy NGC 253. The scan covers the frequency band from 129.1 to 175.2 GHz, i.e., most of the 2 mm atmospheric window. We identify 111 spectral features as transitions from 25 different molecular species. Eight of which (three tentatively) are detected for the first time in the extragalactic interstellar medium. Among these newly detected species, we detected the rare isotopomers 34SO and HC 18O+. Tentative detections of two deuterated species, DNC and N2D+, are reported for the first time from a target beyond the Magellanic Clouds. In addition, three hydrogen recombination lines are identified, while no organic molecules larger than methanol are detected. Column densities and rotation temperatures are calculated for all the species, including an upper limit to the ethanol abundance. A comparison of the chemical composition of the nuclear environment of NGC 253 with those of selected nearby galaxies demonstrates the chemical resemblance of IC 342 and NGC 4945 to that of NGC 253. On the other hand, the chemistries characterizing NGC 253 and M82 are clearly different. We also present a comparison of the chemical composition of NGC 253 with those observed in Galactic prototypical sources. The chemistry of NGC 253 shows a striking similarity with the chemistry observed toward the Galactic center molecular clouds, which are thought to be dominated by low-velocity shocks. This resemblance strongly suggests that the heating in the nuclear environment of NGC 253 is dominated by the same mechanism as that in the central region of the Milky Way. © 2006. The American Astronomical Society. All rights reserved., J.M. P. has been partially supported by the Spanish Ministerio de Educacion y Ciencia under projects ESP 2004-00665, AYA 2002-10113-E and AYA 2003-02785-E. S. G. B. acknowledges financial support from AYA2003-07584 and ESP 2003-04957.