We have obtained 48 high resolution echelle spectra of the pre-main sequence eclipsing binary system KH 15D (V582 Mon, P = 48.37 d, e ~ 0.6, M_A = 0.6 solar masses, M_B = 0.7 solar masses).  The eclipses are caused by a circumbinary disk seen nearly edge on, which at the epoch of these observations completely obscured the orbit of star B and a large portion of the orbit of star A.  These 48 spectra were obtained over five contiguous observing  seasons from 2001/2002 to 2005/2006 and while star A was fully visible, fully occulted, and during several ingress and egress events.  The H-alpha line profile shows strong changes in these time series data over timescales ranging from days to years.  A fraction of the variations are due to "edge effects" and depend only on the height of star A above or below the occulting disk.  Other observed variations depend on the orbital phase in the sense that the H-alpha emission line profile changes from an inverse P-Cygni type profile during ingress to an enhanced, double-peaked profile, with both a blue and red emission component during egress.  We find that these observations can be accurately explained within the context of circumbinary accretion and gas flows in close T Tauri star binaries as predicted by the models put forward by Artymowicz & Lubow, Gunther & Kley, and de Val Borro and coworkers.