The third observing run by LVC has brought the discovery of many compact binary coalescences. Following the detection of the first binary neutron star merger in this run (LIGO/Virgo S190425z), we performed a dedicated follow-up campaign with the Zwicky Transient Facility (ZTF) and Palomar Gattini-IR telescopes. The initial skymap of this single-detector gravitational wave (GW) trigger spanned most of the sky observable from Palomar Observatory. Covering 8000 deg2 of the initial skymap over the next two nights, corresponding to 46% integrated probability, ZTF system achieved a depth of ≈21 m AB in g-and r-bands. Palomar Gattini-IR covered 2200 square degrees in J-band to a depth of 15.5 mag, including 32% integrated probability based on the initial skymap. The revised skymap issued the following day reduced these numbers to 21% for the ZTF and 19% for Palomar Gattini-IR. We narrowed 338,646 ZTF transient "alerts" over the first two nights of observations to 15 candidate counterparts. Two candidates, ZTF19aarykkb and ZTF19aarzaod, were particularly compelling given that their location, distance, and age were consistent with the GW event, and their early optical light curves were photometrically consistent with that of kilonovae. These two candidates were spectroscopically classified as young core-collapse supernovae. The remaining candidates were ruled out as supernovae. Palomar Gattini-IR did not identify any viable candidates with multiple detections only after merger time. We demonstrate that even with single-detector GW events localized to thousands of square degrees, systematic kilonova discovery is feasible.