Dark and baryonic matter moved at different velocities in the early Universe, which strongly suppressed star formation in some regions(1). This was estimated(2) to imprint a large-scale fluctuation signal of about two millikelvin in the 21-centimetre spectral line of atomic hydrogen associated with stars at a redshift of 20, although this estimate ignored the critical contribution of gas heating due to X-rays(3,4) and major enhancements of the suppression. A large velocity difference reduces the abundance of haloes(1,5,6) and requires the first stars to form in haloes of about a million solar masses(7,8), substantially greater than previously expected(9,10). Here we report a simulation of the distribution of the first stars at redshift 20 (cosmic age of around 180 million years), incorporating all these ingredients within a 400-megaparsec box. We find that the 21-centimetre hydrogen signature of these stars is an enhanced (ten millikelvin) fluctuation signal on the hundred-megaparsec scale, characterized(2) by a flat power spectrum with prominent baryon acoustic oscillations. The required sensitivity to see this signal is achievable with an integration time of a thousand hours with an instrument like the Murchison Wide-field Array(11) or the Low Frequency Array(12) but designed to operate in the range of 50-100 megahertz.