||The successful synthesis of ZnCu3(OH)6Cl2 has provided a long-awaited opportunity to test experimentally the physics of spin-1/2 Heisenberg antiferromagnet on the kagomé lattice, which is a frustrated network with a low coordination number. The compound has a coupling constant J ~ 170K, and it does not show any magnetic order down to 50mK. However, from electron spin resonance (ESR), the Dzyaloshinskii-Moriya (DM) interactions which favor the three-sublattice Q = 0 Néel order, are found to be present, with strength D ~ 0.08J. By using exact diagonalization, we obtain the low-lying spectra of the spin Hamiltonian on periodic clusters up to 36 sites. We also calculate the sublattice moment in each cluster. Then with finite-size scaling, we argue that in the thermodynamic limit, the Heisenberg antiferromagnet with DM interactions undergoes a quantum phase transition at Dc ~ 0.1J. For D < Dc, the system has no magnetic long-range order; for D > Dc, it develops the Q = 0 Néel order. Our results are therefore compatible with the absence of Néel-type order found experimentally in ZnCu3(OH)6Cl2, where D is only ~ 0.08J.