We present the first results of a targeted survey carried out with the 305 m Arecibo telescope to detect H I line emission from galaxies at redshift z > 0.16. The targets, selected from the Sloan Digital Sky Survey database, are noninteracting disk galaxies in relatively isolated fields. We present here the H I spectra and derived H I parameters for 10 objects detected in this pilot program. All are massive disk galaxies in the redshift interval 0.17-0.25 (i.e., 2-3 Gyr look-back time), with H I masses M(HI) = (3-8) x 10(10) M(circle dot) and high gas mass fractions (H I-to-stellar mass ratios similar to 10%-30%). Our results demonstrate the efficacy of exploiting Arecibo's large collecting area to measure the H I mass and rotational velocity of galaxies above redshift. In particular, z = 0.2 this sample includes the highest redshift detections of H I emission from individual galaxies made to date. Extension of this pilot program will allow us to study the H I properties of field galaxies at cosmological distances, thus complementing ongoing radio synthesis observations of cluster samples at z similar to 0.2.