We report observations of the He I λ5876 (D3) line in the late A- and early F-type stars in the Hyades, Praesepe, and Coma star clusters used to determine chromospheric activity levels. The average activity level in the early F-type stars is statistically identical in the three clusters and in field dwarfs, and the dispersion in activity levels in each sample is similar. The earliest star detected in each cluster ranges from B-V = 0.26 in the Hyades to B-V = 0.31 in Praesepe. However, four stars in the Hyades in the range 0.28-0.32 are not detected. The detection of Hyades star VB 84 at B-V = 0.26 represents the bluest star observed to date with a statistically nonzero chromospheric D3 equivalent width. In nine early F-type stars we compare D3 strength either during two different observing runs or in several individual integrations. In two stars we find evidence for short-term variability of a factor of 2 on timescales of 1 day or less. The timescale of the variability is consistent with rotational modulation. Finally, the similarity in chromospheric activity in the Hyades and Praesepe stars contrasts with the significant weakness of coronal X-ray emission of early F-type stars in Praesepe compared to Hyades. We have no explanation for this difference; however, this result suggests that the observed disappearance of D3 in the late A-type stars is not directly caused by the weak coronal emission of these stars.