We demonstrate that a beam of x-ray radiation can be generated by simply focusing a single high-intensity laser pulse into a gas jet. A millimeter-scale laser-produced plasma creates, accelerates, and wiggles an ultrashort and relativistic electron bunch. As they propagate in the ion channel produced in the wake of the laser pulse, the accelerated electrons undergo betatron oscillations, generating a femtosecond pulse of synchrotron radiation, which has keV energy and lies within a narrow (50 mrad) cone angle.