We utilize the new Magellan adaptive optics system (MagAO) to image the binary proplyd LV 1 in the Orion Trapezium at H alpha. This is among the first AO results in visible wavelengths. The H alpha image clearly shows the ionization fronts, the interproplyd shell, and the cometary tails. Our astrometric measurements find no significant relative motion between components over ~18 yr, implying that LV 1 is a low-mass system. We also analyze Large Binocular Telescope AO observations, and find a point source which may be the embedded protostar's photosphere in the continuum. Converting the H magnitudes to mass, we show that the LV 1 binary may consist of one very-low-mass star with a likely brown dwarf secondary, or even plausibly a double brown dwarf. Finally, the magnetopause of the minor proplyd is estimated to have a radius of 110 AU, consistent with the location of the bow shock seen in H alpha. ; Comment: 12 pages, 3 figures. Published in Astrophysical Journal