We have measured and analyzed the resistivity and voltage-current characteristics of the charge-ordered organic salt theta-(BEDT-TTF)(2)CsM(SCN)(4) (M = Zn, Co, and Co(0.7)Z(0.3)). At 4.3 K, all the samples show giant nonlinear conduction, in which the c-axis resistivity markedly decreases with external current by a factor of 10 against a small electric field of 1 V/cm. The temperature dependence of the resistivity is well described by an activation law, the activation energy of which is evaluated to be 2 meV in the low-current limit, and linearly decreases with external current. The activation energy and x-ray intensity near q(2) = (0, k, 1/2) are found to show the same dependence on current density. This coincidence strongly suggests that the energy gap of the charge order indexed by q(2) is an order parameter of this phenomenon.