This Letter reports the first scientific results from the observation of antineutrinos emitted by fission products of ^{235}U at the High Flux Isotope Reactor. PROSPECT, the Precision Reactor Oscillation and Spectrum Experiment, consists of a segmented 4 ton ^{6}Li-doped liquid scintillator detector covering a baseline range of 7-9 m from the reactor and operating under less than 1 m water equivalent overburden. Data collected during 33 live days of reactor operation at a nominal power of 85 MW yield a detection of 25 461±283 (stat) inverse beta decays. Observation of reactor antineutrinos can be achieved in PROSPECT at 5σ statistical significance within 2 h of on-surface reactor-on data taking. A reactor model independent analysis of the inverse beta decay prompt energy spectrum as a function of baseline constrains significant portions of the previously allowed sterile neutrino oscillation parameter space at 95% confidence level and disfavors the best fit of the reactor antineutrino anomaly at 2.2σ confidence level.