The best X-ray position (Einstein Observatory HRI - Giacconi et al 1979) for LMC X-3 confirms its identification with the early type star first suggested by Warren and Penfold (1975). Our spectroscopic observations obtained with the CTIO 4–m telescope show the WP star is a slightly reddened B3 V star with mV ≈ 16.9. Large radial velocity variations (Δv ≈ 500 km s−1) reveal an orbital period of 1.7049 days. From the orbital elements (Table 1) one can determine the mass function f(M) = (Mx sin i)3/(Mopt + Mx)2 = 2.3 M⊙, which shows without any assumptions about the mass of the optical star, the orbital inclination, or the mass ratio the unseen X-ray object has a mass >2.3 M⊙. Detailed analysis of the HEAO–1 scanning modulation collimator X-ray data shows that the system does not eclipse, implying that the orbital inclination is ≤ 65°. Assuming the B star mass lies between 4 and 8 M⊙ (an average mass for a normal B3 V star would be about 6–7 M⊙), the mass of the unseen companion must lie between 7 and 13 M⊙ (see Fig. 4a - Hutchings, this volume). Smaller inclinations of course give even higher masses. An important point is that the unseen star must have a mass larger than that of the B star, and thus if it were any kind of normal star it should be easily seen in the spectrum. Thus the X-ray emitting object is a very good candidate for a black hole.