High-cadence observations by the slit-jaw (SJ) optics system of the sounding rocket experiment known as the Chromospheric Lyman Alpha Spectropolarimeter (CLASP) reveal ubiquitous intensity disturbances that recurrently propagate in either the chromosphere or the transition region or both at a speed much higher than the speed of sound. The CLASP/SJ instrument provides a time series of two-dimensional images taken with broadband filters centered on the Lyα line at a 0.6 s cadence. The multiple fast-propagating intensity disturbances appear in the quiet Sun and in an active region, and they are clearly detected in at least 20 areas in a field of view of 527″ × 527″ during the 5 minute observing time. The apparent speeds of the intensity disturbances range from 150 to 350 km s-1, and they are comparable to the local Alfvén speed in the transition region. The intensity disturbances tend to propagate along bright elongated structures away from areas with strong photospheric magnetic fields. This suggests that the observed fast-propagating intensity disturbances are related to the magnetic canopy structures. The maximum distance traveled by the intensity disturbances is about 10″, and the widths are a few arcseconds, which are almost determined by a pixel size of 1.″03. The timescale of each intensity pulse is shorter than 30 s. One possible explanation for the fast-propagating intensity disturbances observed by CLASP is magnetohydrodynamic fast-mode waves.