Context. NGC 2004#115 was classified as a single lined (SB1) Be spectroscopic binary in the Large Magellanic Cloud. Its HΞ± morphology is reminiscent of the Galactic systems LB-1 and HR 6819, both of which are proposed as either Be+BH or Be+stripped He-star systems. Aims. Multi-epoch optical spectra of NGC 2004#115 are used to determine if this binary can be explained by either of these two scenarios, and hence shed additional light on these interesting systems. Methods. VLT-FLAMES and SALT-HRS data covering a baseline of βΌ20 years were analyzed to determine radial velocities and orbital parameters, while non-LTE model atmospheres were used to determine stellar parameters and the relative brightness of the system components. Archive MACHO, Gaia, and XMM-Newton data provide additional constraints on the system. Results. NGC 2004#115 is found to be a triple system consisting of an inner binary with a period P=2.92 d, eccentricity e βΌ0.0, and mass function f =0.07 M . The only firmly detected star in this inner binary is a B2 star, the primary, with a projected rotational velocity (v e sin i) of 10 km s β1 and a luminosity of log L/L =3.87. It contributes βΌ 60% of the total V-band light, with the tertiary contributing the other βΌ 40% of the light, while the secondary is not detected in the optical spectrum. The possibility that the primary is a low mass inflated stripped star is excluded since its Roche radius would be smaller than its stellar radius in such a compact system. A main sequence star of mass 8.6 M is therefore inferred; however, the assumption of synchronous rotation leads to a secondary mass in excess of 25 M , which would therefore be a black hole. The tertiary is detected as a fainter blended component to the hydrogen and helium lines, which is consistent with a slightly less massive B-type star, though with v e sin iβΌ300 km s β1 . The data do not permit the characterization of the outer period, though it likely exceeds 120 days and is therefore in a stable configuration. The disk-like emission is variable, but may be associated with the inner binary rather than the rapidly rotating tertiary. XMM-Newton provides an upper limit of 5 Γ 10 33 ergs s β1 in the 0.2-12 keV band which is consistent with, though not constraining, the system hosting a quiescent B+BH binary. A number of caveats to this scenario are discussed.