We have studied a highly variable ultraluminous X-ray source (ULX) in the Fornax galaxy NGC 1365, with a series of 12 Chandra and XMM-Newton observations between 2002 and 2006. In 2006 April, the source peaked at a luminosity ~ 3 x 10^{40} erg/s in the 0.3-10 keV band (similar to the maximum luminosity found by ASCA in 1995), and declined on an e-folding timescale ~ 3 days. The X-ray spectrum is always dominated by a broad power-law-like component. When the source is seen at X-ray luminosities ~ 10^{40} erg/s, an additional soft thermal component (which we interpret as emission from the accretion disk) contributes ~ 1/4 of the X-ray flux; when the luminosity is higher, ~ 3 x 10^{40} erg/s, the thermal component is not detected and must contribute < 10% of the flux. At the beginning of the decline, ionized absorption is detected around 0.5-2 keV; it is a possible signature of a massive outflow. The power-law is always hard, with a photon index Gamma ~ 1.7 (and even flatter at times), as is generally the case with bright ULXs. We speculate that this source and perhaps most other bright ULXs are in a high/hard state: as the accretion rate increases well above the Eddington limit, more and more power is extracted from the inner region of the inflow through non-radiative channels, and is used to power a Comptonizing corona, jet or wind. The observed thermal component comes from the standard outer disk; the transition radius between outer standard disk and Comptonizing inner region moves further out and to lower disk temperatures as the accretion rate increases. This produces the observed appearance of a large, cool disk. Based on X-ray luminosity and spectral arguments, we suggest that this accreting black hole has a likely mass ~ 50-150 Msun (even without accounting for possible beaming).
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