We report on a new search for solar chameleons with the CERN Axion Solar Telescope (CAST). A GridPix detector was used to search for soft X-ray photons in the energy range from 200 eV to 10 keV from converted solar chameleons. No significant excess over the expected background has been observed in the data taken in 2014 and 2015. We set an improved limit on the chameleon photon coupling, βγ#5.7×1010 for 1<βm<106 at 95% C.L. improving our previous results by a factor two and for the first time reaching sensitivity below the solar luminosity bound for tachocline magnetic fields up to 12.5 T.