In preparation for the full Arecibo Legacy Fast ALFA (ALFALFA) extragalactic H I survey, precursor observations were carried out in 2004 August - September with the seven-beam Arecibo L-band Feed Array (ALFA) receiver system and the Wideband Arecibo Pulsar Processor spectral processors. While these observations were geared mainly at testing and debugging survey strategy, hardware, and software, approximately 48 hr of telescope time yielded science-quality data. The efficiency of system usage (allowing for minor malfunctions and the impact of radio-frequency interference) during that time was 75%. From those observations, an initial list of 730 tentative detections of varying degrees of reliability was extracted. Ninety-eight high signal-to-noise ratio candidates were deemed to be bona fide H I line detections. To test our ability to discriminate cosmic signals from radio-frequency interference and noise, 165 candidates ranging in reliability likelihood were reobserved with the single-beam L-band wide system at Arecibo in 2005 January - February. Of those, 41% were confirmed as real. We present the results of both the ALFA and the single-beam observations for the sample of 166 confirmed H I sources, as well as our assessment of their optical counterparts. Of the 166 sources, 62 coincided with previously known H I sources, while optical redshifts were available for an additional 18 galaxies; thus, 52% of the redshifts reported here were previously unknown. Of the 166 H I detections, 115 are identified with previously cataloged galaxies of either known or unknown redshift, leaving 51 objects identified for the first time. Because of the higher sensitivity of the Arecibo system, fewer than 10% of the 166 H I sources would have been detected by a HIPASS-like survey of the same region. Three of the objects have H I masses less than 107 M ⊙. The full ALFALFA survey, which commenced in 2005 February, should detect more than 100 times as many objects of similarly low H I mass over the next 5 years.