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Summary form only given. Diode-pumped microchip laser arrays have attracted increasing interest because of their high beam quality, compactness and power scalability. The brightness of the array laser output increases when the output powers from individual single transverse mode lasers are coherently combined. One of the useful techniques for phase-locking a laser array is the Talbot effect, which refers to a diffraction phenomenon where by exact images of an infinite periodic object are formed at certain distances away from the object plane. The coupling by the use of Talbot is a simple self-consistent technique that uses only a two mirror cavity separated by 1/4 Talbot distance. Although a variety of nonlinear dynamics in laser arrays have been reported, the stability of laser arrays with a Talbot cavity has not been investigated yet. We experimentally observed chaotic oscillations of a diode-pumped Nd:YAG microchip laser array with an auxiliary external mirror at a Talbot distance (30 cm) from the laser crystal.