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Context. NGC 300 X-1 is the second extragalactic candidate, after IC 10 X-1,in the rare class of Wolf-Rayet/compact object X-ray binary systems exemplifiedin the Galaxy by Cyg X-3. From a theoretical point of view, accretion onto ablack hole in a detached system is possible for large orbital periods only ifthe mass of the relativistic object is high or the velocity of the accretedwind is low. Aims. We analysed a 2 week SWIFT XRT light curve of NGC 300 X-1and searched for periodicities. Methods. Period searches were made usingLomb-Scargle periodogram analysis. We evaluated the confidence level usingMonte Carlo simulations. Results. A period of 32.8+-0.4h (3 sigma error) wasfound for NGC 300 X-1 with a confidence level >99%. Furthermore, we confirm thehigh irregular variability during the high flux level, as already observed inthe XMM-Newton observations of the source. A folded XMM-Newton light curve isshown, with a profile that is in agreement with SWIFT. The mean absorbed X-rayluminosity in the SWIFT observations was 1.5x10^38 erg/s, close to the valuederived from the XMM-Newton data. Conclusions. While Cyg X-3 has a short periodof 4.8 h, the period of NGC 300 X-1 is very close to that of IC 10 X-1(34.8+-0.9 h). These are likely orbital periods. Possibility of formation ofaccretion disk for such high orbital periods strongly depends on the terminalvelocity of the Wolf-Rayet star wind and black-hole mass. While low masses arepossible for wind velocities < 1000 km/s, these increase to several tens ofsolar masses for velocities > 1600 km/s and no accretion disk may form forterminal velocities larger than 1900 km/s.Comment: 4 pages, 6 figures, accepted as a Letter in Astronomy & Astrophysics.  Figure 6 will appear with a better quality in the A&A pape

A 33 hour period for the Wolf-Rayet/black hole X-ray binary candidate NGC 300 X-1