At separations below 100 nm, Casimir-Lifshitz forces strongly influence the actuation dynamics of microelectromechanical systems (MEMS) in dry vacuum conditions. For a micron-size plate oscillating near a surface, which mimics a frequently used setup in experiments with MEMS, we show that the roughness of the surfaces significantly influences the qualitative dynamics of the oscillator. Via a combination of analytical and numerical methods, it is shown that surface roughness leads to a clear increase of initial conditions associated with chaotic motion, that eventually lead to stiction between the surfaces. Since stiction leads to a malfunction of MEMS oscillators, our results are of central interest for the design of microdevices. Moreover, stiction is of significance for fundamentally motivated experiments performed with MEMS.