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We study neutron-proton equilibration in dynamically deformed atomic nuclei created in nuclear collisions. The two ends of the elongated nucleus are initially dissimilar in composition and equilibrate on a subzeptosecond time scale following first-order kinetics. We use angular momentum to relate the breakup orientation to the time scale of the breakup. The extracted rate constant is 3  zs^{-1}, which corresponds to a mean equilibration time of 0.3 zs. This technique enables new insight into the nuclear equation of state that governs many nuclear and astrophysical phenomena leading to the origin of the chemical elements.