Polar rain is usually a weak, diffuse precipitation of electrons with intensities below 0.1 erg/cm² s and temperatures around 80 eV. Occasionally, it can have much higher fluxes and temperatures. We carried out an investigation using an automated search of the DMSP F7 polar cap precipitation over a 1100‐day interval to find all the days with reasonably intense (>106 eV/cm² s sr) fluxes in one or more ≥1‐keV electron channels above 80 MLAT. After we eliminated precipitation associated with polar cap arcs, 17 such days were found. For 11 days, the precipitation was at least 0.4 erg/cm² s, and on 4 days it reached a few ergs/cm² s (for example, n = 0.85/cm³, and kT = 2000 eV). A fairly uniform polar rain over the polar caps at this intensity approximately equals the hemispherical energy flux over the entire auroral oval. Like ordinary polar rain, the keV precipitation occurs in only one hemisphere and is generally accompanied by an often high‐density polar rain at more typical energies. No particular association with storms or poststorm quieting was evident in our sample; instead, the results appear to be consistent with the model of Fairfield and Scudder, in that there is an apparent association between intense keV polar rain and low solar‐wind densities. The keV electrons were not observed within the cusp proper, further supporting the concept of polar rain as a special component of the solar‐wind electron population. A persistent gap between the poleward edge of auroral electron precipitation and the occurrence of polar rain is observed; the gap is largest at dusk, smaller at dawn, still smaller near midnight, and nonexistent on the dayside. We interpret the field lines poleward of the auroraloval precipitation and equatorward of polar rain as recently closed field lines.