Reactor antineutrinos are used to study neutrino oscillation, search for signatures of non-standard neutrino interactions, and to monitor reactor operation for safeguard applications. The flux and energy spectrum of reactor antineutrinos can be predicted from the decays of the nuclear fission products. A comparison of recent reactor calculations with past measurements at baselines of 10-100m suggests a 5.7% deficit. Precision measurements of reactor antineutrinos at very short baselines O(1-10 m) can be used to probe this anomaly and search for possible oscillations into sterile neutrino species. This paper studies the experimental requirements for a new reactor antineutrino measurement at very short baselines and calculates the sensitivity of various scenarios. We conclude that an experiment at a typical research reactor provides 5{sigma} discovery potential for the favored oscillation parameter space with 3 years of data collection.