High-resolution spectroscopic observations were taken of 29 extended main-sequence turnoff (eMSTO) stars in the young (similar to 200 Myr) Large Magellanic Cloud (LMC) cluster, NGC 1866, using the Michigan/Magellan Fiber System and MSpec spectrograph on the Magellan-Clay 6.5 m telescope. These spectra reveal the first direct detection of rapidly rotating stars whose presence has only been inferred from photometric studies. The eMSTO stars exhibit Ha emission (indicative of Be-star decretion disks), others have shallow broad H alpha absorption (consistent with rotation. greater than or similar to 150 km s(-1)), or deep Ha core absorption signaling lower rotation velocities (less than or similar to 150 km s(-1)). The spectra appear consistent with two populations of stars-one rapidly rotating, and the other, younger and slowly rotating.