We have monitored a sample of 27 nearby globular clusters in the hard X-ray band (20-120 keV) for ˜1400 days using the BATSE instrument on board the Compton Gamma Ray Observatory. Globular clusters may contain a large number of compact objects (e.g., pulsars or X-ray binaries containing neutron stars) that can produce hard X-ray emission. Our search provides a sensitive (˜50 mCrab) monitor for hard X-ray transient events on timescales of ≥ 1 day, as well as a means for observing persistent hard X-ray emission. We have discovered no transient events from any of the clusters and no persistent emission. Our observations include a sensitive search of four nearby clusters containing dim X-ray sources: 47 Tucanae, NGC 5139, NGC 6397, and NGC 6752. The nondetection in these clusters implies a lower limit for the recurrence time of transients of 2-6 yr for events with luminosities ≥1036 ergs s-1 (20-120 keV) and ˜20 yr if the sources in these clusters are taken collectively. This suggests that the dim X-ray sources in these clusters are not transients similar to Aql X-1. We also place upper limits on the persistent emission in the range (2-10) × 1034 ergs s-1 (2 σ, 20-120 keV) for these four clusters. For 47 Tuc, the upper limit is more sensitive than previous measurements by a factor of 3. We find a model-dependent upper limit of 19 isolated millisecond pulsars producing gamma rays in 47 Tuc, compared to the 11 observed radio millisecond pulsars in this cluster.