We have searched for mixing in the D(0)-D (0) system by measuring the decay-time distribution of D(0) --> K(+) pi(-) decays. The analysis uses 90 fb(-1) of data collected by the Belle detector at the KEKB e(+) e(-) collider. We fit the decay-time distribution for the mixing parameters x' and y' and also for the parameter R(D), which is the ratio of the rate for the doubly-Cabibbo-suppressed decay D(0)--> K+ pi(-) to that for the Cabibbo-favored decay D(0)--> K-pi(+). We do these fits both assuming CP conservation and allowing for CP violation. We use a frequentist method to obtain a 95% C.L. region in the x'(2) - y' plane. Assuming no mixing, we measure R(D) = (0.381 +/- 0.017(+0.008)(-0.016))%.