Energy storage is the main challenge for a deep penetration of renewable energies into the grid to overcome their intrinsic variability. Thus, the commercial expansion of renewable energy, particularly wind and solar, at large scale depends crucially on the development of cheap, efficient and non-toxic energy storage systems enabling to supply more flexibility to the grid. The Ca-Looping (CaL) process, based upon the reversible carbonation/calcination of CaO, is one of the most promising technologies for thermochemical energy storage (TCES), which offers a high potential for the long-term storage of energy with relatively small storage volume. This manuscript explores the use of the CaL process to store Concentrated Solar Power (CSP). A CSP-CaL integration scheme is proposed mainly characterized by the use of a CO2 closed loop for the CaL cycle and power production, which provides heat decoupled from the solar source and temperatures well above the 550 C limit that poses the use of molten salts currently used to store energy as sensible heat. The proposed CSP-CaL integration leads to high values of plant global efficiency (of around 45-46%) with a storage capacity that allows for long time gaps between load and discharge. Moreover, the use of environmentally benign, abundantly available and cheap raw materials such as natural limestone would mark a milestone on the road towards the industrial competitiveness of CSP