We use the Wide Field Camera 3 on the Hubble Space Telescope to spectrophotometrically monitor the young L7.5 companion HD 203030B . Our time series reveal photometric variability at 1.27 \mu m and 1.39 \mu m on time scales compatible with rotation . We find a rotation period of 7.5 ^ { +0.6 } _ { -0.5 } h : comparable to those observed in other brown dwarfs and planetary-mass companions younger than 300 Myr . We measure variability amplitudes of 1.1 \pm 0.3 \% ( 1.27 \mu m ) and 1.7 \pm 0.4 \% ( 1.39 \mu m ) , and a phase lag of 56 ^ { \circ } \pm 28 ^ { \circ } between the two light curves . We attribute the difference in photometric amplitudes and phases to a patchy cloud layer that is sinking below the level where water vapor becomes opaque . HD 203030B and the few other known variable young late-L dwarfs are unlike warmer ( earlier-type and/or older ) L dwarfs , for which variability is much less wavelength-dependent across the 1.1–1.7 \mu m region . We further suggest that a sinking of the top-most cloud deck below the level where water or carbon monoxide gas become opaque may also explain the often enhanced variability amplitudes of even earlier-type low-gravity L dwarfs . Because these condensate and gas opacity levels are already well-differentiated in T dwarfs , we do not expect the same variability amplitude enhancement in young vs. old T dwarfs .