Electron cyclotron maser emission is an accepted physical mechanism for generating coherent planetary and stellar radio emissions. Observational data has indicated evidence of nonlinear and chaotic temporal variability in some cosmic masers such as solar microwave spikes. The nonlinear and chaotic characteristics of cosmic masers can be attributed to plasma turbulence, such as Alfvén chaos, embedded in the emission region. We report a chaos theory of Alfvén waves which can account for chaotic acceleration of electrons in the source region of cosmic masers. Two types of Alfvén intermittency are identified: Pomeau-Manneville intermittency and crisis-induced intermittency. Since Alfvén waves may be responsible for accelerating electrons that emit maser radiations, the chaotic dynamics of Alfvén waves may be the origin of chaotic time variations of cosmic masers. Hence, we suggest that Alfvén intermittency may cause intermittent temporal fluctuations which can be observed in cosmic masers.