We present the results of a systematic search for Ly alpha emitters (LAEs) at 6 less than or similar to z less than or similar to 7.6 using the HST WFC3 Infrared Spectroscopic Parallel (WISP) Survey. Our total volume over this redshift range is similar to 8 x 10(5) Mpc(3), comparable to many of the narrowband surveys despite their larger area coverage. We find two LAEs at z = 6.38 and 6.44 with line luminosities of L-Lya similar to 4.7 x 10(43) erg s(-1), putting them among the brightest LAEs discovered at these redshifts. Taking advantage of the broad spectral coverage of WISP, we are able to rule out almost all lower-redshift contaminants. The WISP LAEs have a high number density of 7.7 x 10(-6) Mpc (3). We argue that the LAEs reside in megaparsec-scale ionized bubbles that allow the Ly alpha photons to redshift out of resonance before encountering the neutral intergalactic medium. We discuss possible ionizing sources and conclude that the observed LAEs alone are not sufficient to ionize the bubbles.