We describe a method for obtaining a flux-limited sample of Ly-alpha emitters from GALEX grism data. We show that the multiple GALEX grism images can be converted into a three-dimensional (two spatial axes and one wavelength axis) data cube. The wavelength slices may then be treated as narrowband images and searched for emission-line galaxies. For the GALEX NUV grism data, the method provides a Ly-alpha flux-limited sample over the redshift range z=0.67-1.16. We test the method on the Chandra Deep Field South field, where we find 28 Ly-alpha emitters with faint continuum magnitudes (NUV>22) that are not present in the GALEX pipeline sample. We measure the completeness by adding artificial emitters and measuring the fraction recovered. We find that we have an 80% completeness above a Ly-alpha flux of 10^-15 erg/cm^2/s. We use the UV spectra and the available X-ray data and optical spectra to estimate the fraction of active galactic nuclei in the selection. We report the first detection of a giant Ly-alpha blob at z<1, though we find that these objects are much less common at z=1 than at z=3. Finally, we compute limits on the z~1 Ly-alpha luminosity function and confirm that there is a dramatic evolution in the luminosity function over the redshift range z=0-1.
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