We report the results of a study which assembles deep observations with the ACIS-I instrument on the Chandra Observatory to study the evolution in the core properties of a sample of galaxy groups and clusters out to redshifts z ≈ 1.3. A search for extended objects within these fields yields a total of 62 systems for which redshifts are available, and we added a further 24 non-X-ray-selected clusters, to investigate the impact of selection effects and improve our statistics at high redshift. Six different estimators of cool core strength are applied to these data: the entropy (K) and cooling time (t cool ) within the cluster core, the cooling time as a fraction of the age of the Universe (t cool /t Uni ), and three estimators based on the cuspiness of the X-ray surface brightness profile. A variety of statistical tests are used to quantify evolutionary trends in these cool core indicators. In agreement with some previous studies, we find that there is significant evolution in t cool /t Uni , but little evolution in t cool , suggesting that gas is accumulating within the core, but that the cooling time deep in the core is controlled by AGN feedback. We show that this result extends down to the group regime and appears to be robust against a variety of selection biases (detection bias, archival biases and biases due to the presence of central X-ray AGN) which we consider. Recent results (Semler et al. 2012;McDonald et al. 2013) based on samples of clusters selected by the Sunyaev-Zeldovich (SZ) effect, with Chandra follow-up, demonstrate that CC clusters do exist at redshifts greater than 0.5. Moreover, McDonald et al. (2013) found that there is no evolution in central cooling time out to redshifts ∼ 1. There are also studies on individual clusters, although not very numerous, which show that there are strong cool cores at high redshift. The WARPS cluster studied by Santos et al. (2012) is a CC cluster at redshift 1.03. Another interesting system is 3C188, studied by Siemiginowska et al. (2010), which is a strong CC system at z=1.03 with a powerful radio AGN at its centre. Signs of cooling at the centre of the cluster surrounding the z = 1.04 powerful quasar PKS1229-021 have also been reported by Russell et al. (2012).While most of these evolutionary studies have concentrated on rich clusters, and show a reduction in the incidence of strong CCs at