The maximized hyperbolic space of a right-angled Coxeter group (RACG) can be obtained from its Davis complex by coning off all standard flats. This space serves as the top-level hyperbolic space in the hierarchically hyperbolic structure of the RACG, analogous to the curve graph for mapping class groups. We provide a necessary and sufficient condition on the defining graph under which the Gromov boundary of the maximized hyperbolic space is connected.