Crystal and magnetic structures of the mineral centennialite CaCu3(OH)6Cl2·0.6H2O are investigated by means of synchrotron X-ray diffraction and neutron diffraction measurements complemented by density functional theory (DFT) and pseudofermion functional renormalization group (PFFRG) calculations. CaCu3(OH)6Cl2·0.6H2O crystallizes in the P3m1 space group and Cu2+ ions form a geometrically perfect kagome network with antiferromagnetic J1. No intersite disorder between Cu2+ and Ca2+ ions is detected. CaCu3(OH)6Cl2·0.6H2O enters a magnetic long-range ordered state below TN=7.2 K, and the q=0 magnetic structure with negative vector spin chirality is obtained. The ordered moment at 0.3 K is suppressed to 0.58(2)μB. Our DFT calculations indicate the presence of antiferromagnetic J2 and ferromagnetic Jd superexchange couplings of a strength which places the system at the crossroads of three magnetic orders (at the classical level) and a spin-12 PFFRG analysis shows a dominance of q=0 type magnetic correlations, consistent with and indicating proximity to the observed q=0 spin structure. The results suggest that this material is located close to a quantum critical point and is a good realization of a J1-J2-Jd kagome antiferromagnet. © 2020 American Physical Society.