This paper describes a millimicrosecond timing apparatus for determining the arrival directions of extensive cosmic‐ray air showers. The apparatus consists of four plastic scintillation detectors in a square array and a fast oscillograph with which one can determine the relative arrival times of the first shower particles which reach the four detectors as indicated by the relative positions of pulses from the detectors on the oscillographic sweep. The uncertainty in determinations of the relative arrival times of the particles in a shower is about 3 millimicroseconds. The uncertainty in the determination of the arrival direction of a shower is about ±5°, and this uncertainty is caused primarily by the lack of coplanarity of the shower particles and not by instrumental limitations.