The concept of fractals provides a means of testing whether clustering in time or space is a scale-invariant process. If the fraction x of the intervals of length T containing earthquakes is related to the time interval by x ~ ד^1-D then fractal clustering is occurring with fractal dimension D (0 < D < 1). We have analyzed a catalog of earthquakes from the New Hebrides for the occurrence of temporal clusters that exhibit fractal behavior. Our studies have considered four distinct regions. The number of earthquakes considered in each region varies from 44 to 1,330. In all cases, significant deviations from random or Poisson behavior are found. The fractal dimensions found vary from 0.126 to 0.255. Our method introduces a new means of quantifying the clustering of earthquakes.