Foreshock disturbances -- large-scale (~1000 km to >30,000 km), transient (~5-10 per day - lasting ~10s of seconds to several minutes) structures [1,2] - generated by suprathermal (>100 eV to 100s of keV) ions [3,4] arise upstream of Earth's bow shock formed by the solar wind colliding with the Earth's magnetosphere. They have recently been found to accelerate ions to energies of several keV [5,6]. Although electrons in Saturn's high Mach number (M > 40) bow shock can be accelerated to relativistic energies (nearly 1000 keV) , it has hitherto been thought impossible to accelerate electrons at the much weaker (M < 20) Earth's bow shock beyond a few 10s of keV . Here we report observations of electrons energized by foreshock disturbances to energies up to at least ~300 keV. Although such energetic electrons have been previously reported, their presence has been attributed to escaping magnetospheric particles [9,10] or solar events . These relativistic electrons are not associated with any solar activity nor are they of magnetospheric origin. Further, current theories of ion acceleration in foreshock disturbances cannot account for electrons accelerated to the observed relativistic energies [12-17]. These electrons are clearly coming from the disturbances, leaving us with no explanation as to their origin.