We present a new model describing the evolution of triple stars which undergo common envelope evolution, using a combination of analytic and numerical techniques. The early stages of evolution are driven by dynamical friction with the envelope, which causes the outer triple orbit to shrink faster than the inner binary. In most cases, this leads to a chaotic dynamical interaction between the three stars, culminating in the ejection of one of the stars from the triple. This ejection and resulting recoil on the remnant binary are sufficient to eject all three stars from the envelope, which expands and dissipates after the stars have escaped. These results have implications for the properties of post-common envelope triples: they may only exist in cases where the envelope was ejected before the onset of dynamical instability, the likelihood of which depends on the initial binary separation and the envelope structure. In cases where the triple becomes dynamically unstable, the triple does not survive and the envelope dissipates without forming a planetary nebula.
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