We present a Cl35 NMR study for the spin S=1/2 perfect kagome antiferromagnet Ca-kapellasite [CaCu3(OH)6Cl2·0.6H2O] with a magnetic transition at T∗=7.2K. The static magnetic structure in the ground state has been determined to be a chirality-ordered Q=0 state, which is selected by a finite Dzyaloshinskii-Moriya interaction. The low-energy magnetic excitations in the ordered state are investigated by a nuclear spin-lattice relaxation rate measurement. We detect a weakly temperature-dependent contribution in the magnetic fluctuations perpendicular to the kagome plane in addition to the dispersive spin-wave contribution in the kagome plane. The low-energy magnetic excitations from the coplanar spin structure are attributed to the zero mode originating from the flat band in this kagome antiferromagnet.