This paper documents on-off intermittency observed in coupled thermoacoustic chaotic oscillations. Mode competition between two or three oscillation modes engenders chaotic oscillations through quasiperiodic oscillations introduced by a local cross-sectional change in a gas-filled tube. Complete synchronization is then obtained by connecting two thermoacoustic chaotic oscillators via a rigid plate with an orifice. From the analysis of pressure fluctuations, theoretical statistical scaling laws related to the laminar phases, spectral density, and amplitude probability distribution are found to be satisfied in the coupled thermoacoustic oscillators, when the thermoacoustic complete synchronization breaks down through an on-off intermittency route with the decreased orifice size.