We probe how common extremely rapid rotation is among massive stars in the early universe by measuring the OBe star fraction in nearby metal-poor dwarf galaxies. We apply a new method that uses broad-band photometry to measure the galaxy-wide OBe star fractions in the Magellanic Clouds and three more distant, more metal-poor dwarf galaxies. We find OBe star fractions of ∼20% in the Large Magallanic Cloud (0.5Zȯ), and ∼30% in the Small Magellanic Cloud (0.2Zȯ) as well as in the so-far unexplored metallicity range 0.1 Z/Zȯ < 0.2 occupied by the other three dwarf galaxies. Our results imply that extremely rapid rotation is common among massive stars in metal-poor environments such as the early universe.