Time-resolved investigation of electron dynamics relies on the generation of isolated attosecond pulses in the (soft) X-ray regime. Thomson scattering is a source of high energy radiation of increasing prevalence in modern labs, complementing large scale facilities like undulators and X-ray free electron lasers. We propose a scheme to generate isolated attosecond X-ray pulses based on Thomson scattering by colliding microbunched electrons on a chirped laser pulse. The electrons collectively act as a relativistic chirped mirror, which superradiantly reflects the laser pulse into a single localized beat. As such, this technique extends chirped pulse compression, developed for radar and applied in optics, to the X-ray regime. In this paper we theoretically show that, by using this approach, attosecond soft X-ray pulses with GW peak power can be generated from pC electron bunches at tens of MeV electron beam energy. While we propose the generation of few cycle X-ray pulses on a table-top system, the theory is universally scalable over the electromagnetic spectrum.