We present high signal-to-noise ratio HST Goddard High Resolution Spectrograph (GHRS) observations of the weak interstellar Kr I λ1236 absorption toward the stars τ CMa, κ Ori, e Ori, λ Ori, δ Sco, ω1 Sco, e Per, and ζ Per. In combination with previous GHRS measurements of Kr I in two other sight lines (ζ Oph and 1 Sco), these new observations yield a mean interstellar gas-phase krypton abundance (per 109 H atoms) of 109 Kr/H = 0.96 ± 0.05. There is no statistically significant variation from sight line to sight line in the measured Kr I abundance and, in particular, no evidence for any correlation with the fraction of hydrogen in molecular form. Since Kr, as a noble gas, is not expected to deplete into dust grains, its gas-phase abundance should reflect the total interstellar abundance. Consequently, the GHRS observations imply that the interstellar Kr abundance in the vicinity of the Sun is about 60% of the solar system value of 109 Kr/H = 1.70 ± 0.30. This interstellar abundance deficit is similar to that recently found for oxygen with GHRS.