We present the first search for the decay B0→KS0KS0KL0 using a data sample of 232×106 BB̄ pairs. We find no statistically significant evidence for the nonresonant component of this decay. Our central value for the branching fraction, assuming the true Dalitz distribution is uniform and excluding the resonance, is B(B0→KS0KS0KL0)=(2.4-2.5+2.7±0.6) ×10-6 where the errors are statistical and systematic, respectively. We set a single-sided Bayesian upper limit of B(B0→KS0KS0KL0)<7.4×10- 6 at 90% confidence level using a uniform prior probability for physical values. Assuming the worst-case true Dalitz distribution, where the signal is entirely in the region of lowest efficiency, the 90% confidence level upper limit is B(B0→KS0KS0KL0)<16×10-6. © 2006 The American Physical Society.