  In this paper, we propose the existence and discuss the properties of rogue
quantum gravitational waves. More specifically, we numerically solve the
Schr\"odinger-Newton system of equations using a spectral scheme with a
$4^{th}$ order Runge-Kutta time integrator and show that noise either imposed
on wave function $\Psi$, or the gravitational field $\Phi$, triggers the
modulation instability which turns the monochromatic wave fields into chaotic
ones exhibiting high and unexpected waves. Such waves can be named as rogue
quantum gravitational waves. We discuss the characteristics and probabilities
of occurrences of such rogue waves in the frame of the Schr\"odinger-Netwon
equations. We suggest alternative methods for studying rogue quantum
gravitational waves and rogue gravitational waves.
