Domain walls (DWs) can be moved very efficiently with nanosecond long current pulses in perpendicularly magnetized Co/Ni/Co nanowires formed with platinum under- and over-layers due to a chiral spin torque mechanism. In these structures the DWs exhibit a chiral Néel structure that has been proposed is set by a Dyzaloshinskii-Moriya exchange interaction (DMI) arising from the Pt/Co and Co/Pt interfaces. The strength of this interaction can be measured from the longitudinal field dependence of the current induced DW velocity. We show, thereby, that the magnitude and sign of the DMI is strongly dependent and monotonically changes as small changes in the thicknesses of the Co layers are made. However, due to the chiral nature of the DMI we show that the magnitude and sign of the DMI is determined by the difference between the respective DMI at the upper and lower interfaces, which compensate each other. Thus, we find that the DMI increases as the lower Co thickness is increased but decreases as the upper Co thickness is increased, changing sign in both cases.