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We have designed and built a self-starting master-slave optoelectronic oscillator without any electronic amplifiers. The optoelectronic oscillator consists of a slave oscillator with 50 m of fiber that is injection-locked by a master oscillator with 2 km of fiber. Both optoelectronic oscillators use the carrier-suppression technique of low-biased Mach-Zehnder modulators to achieve the necessary RF gain for oscillation to occur. The measured RF gain due to this all-photonic technique is as high as 11.5 dB. The timing jitter of the generated 1 GHz signal is 203 fs from 100 Hz to 10 MHz.. This is the first demonstration, to the best of our knowledge, of a low-jitter master-slave optoelectronic oscillator without the need for electronic RF amplifiers in the cavity.