We present results for the nucleon axial charge g_A at a fixed lattice spacing of 1/a=1.73(3) GeV using 2+1 flavors of domain wall fermions on size 16^3x32 and 24^3x64lattices (L=1.8 and 2.7 fm) with length 16 in the fifth dimension. The length of the Monte Carlo trajectory at the lightest m_\pi is 7360 units, including 900 for thermalization. We find finite volume effects are larger than the pion mass dependence at m_\pi= 330 MeV. We also find that g_A exhibits a scaling with the single

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... e m_\pi L which can also be seen in previous two-flavor domain wall and Wilson fermion calculati ons. Using this scaling to eliminate the finite-volume effect, we obtain g_A = 1.20(6)(4) at the physical pion mass, m_\pi = 135 MeV, where the first and second errors are statistical and systematic. The observed finite-volume scaling also appears in similar quenched simulations, but disappear when V\ge (2.4 fm)^3. We argue this is a dynamical quark effect.