Inverse Compton scattering is a promising method to implement a high-brightness, ultra-short, energy tuneable X-ray source at accelerator facilities and at laser facilities using laser wake-field acceleration. We have developed an inverse Compton X-ray source driven by the multi-10-TW laser installed at Daresbury Laboratory. Polarized X-ray pulses will be generated through the interaction of laser pulses with electron bunches delivered by the energy recovery linac commissioned at the ALICE facility with spectral peaks ranging from 0.4 to 12 Å, depending on the electron bunch energy and the scattering geometry. X-ray pulses containing up to 107 photons per pulse will be created from head-on collisions, with a pulse duration comparable to the incoming electron bunch length. For transverse collisions the laser pulse transit time defines the X-ray pulse duration. The peak spectral brightness is predicted to be up to 1021 photon/(s mm2 mrad2 0.1% Δλ/λ). Called COBALD, this source will be initially used as a short-pulse diagnostic for the ALICE electron beam and will explore the extreme challenges of photon/electron beam synchronization, which is a fundamental requirement for all conventional accelerator and laser wake-field-acceleration-based sources.