This article gives a simple and exact method of constructing one-sided tolerance intervals for the case of one-way analysis of variance (ANOVA) with random effects when the variance ratio is known. Because the method developed does not involve any approximations and it retains the maximum possible degrees of freedom, it is superior to any existing methods. Further, the method is applicable for both unbalanced and balanced designs. When the variance ratio is unknown, we suggest an approximate unbiased estimator to be used. Simulations are conducted to indicate the loss in precision with respect to the coverage and the confidence. An example is given to illustrate the methodology.