We present 26 point-sources discovered with Chandra within 200 (~20kpc) of the center of the barred supergiant galaxy NGC 1365. The majority of these sources are high-mass X-ray binaries, containing a neutron star or a black hole accreting from a luminous companion at a sub-Eddington rate. Using repeat Chandra and XMM-Newton as well as optical observations, we discuss in detail the natures of two highly-variable ultraluminous X-ray sources (ULXs): NGC 1365 X1, one of the most luminous ULXs known since the ROSAT era, which is X-ray variable by a factor of 30, and NGC 1365 X2, a newly discovered transient ULX, variable by a factor of >90. Their maximum X-ray luminosities (3-5 x 10^40 erg/s, measured with Chandra) and multiwavelength properties suggest the presence of more exotic objects and accretion modes: accretion onto intermediate mass black holes (IMBHs) and beamed/super-Eddington accretion onto solar-mass compact remnants. We argue that these two sources have black-hole masses higher than those of the typical primaries found in X-ray binaries in our Galaxy (which have masses of <20 Msolar), with a likely black-hole mass of 40-60 Msolar in the case of NGC 1365 X1 with a beamed/super-Eddington accretion mode, and a possible IMBH in the case of NGC 1365 X2 with M=80-500Msolar.
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