A search for a nonrandom component in the cosmic radiation has been conducted using a ground-based air-shower array sensitive to cosmic-ray primaries of energy \ensuremath{\gtrsim}9\ifmmode\times\else\texttimes\fi{}${10}^{14}$ eV. The time interval between the detection of successive air showers has been measured for more than 156 000 air showers recorded over a period of three years. The data are consistent with the conclusion that these primary particles are incident upon the upper atmosphere randomly in time and uniformly from all portions of the sky swept by the array.