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1860, from French claque "band of claqueurs," agent noun from claquer "to clap" (16c.), echoic (cf. clap (v.)). Modern sense of "band of political followers" is transferred from that of "organized applause at theater." Claqueur "audience memeber who gives pre-arranged responses in a theater performance" is in English from 1837.
This method of aiding the success of public performances is very ancient; but it first became a permanent system, openly organized and controlled by the claquers themselves, in Paris at the beginning of the nineteenth century. [Century Dictionary]