The effects of chain architecture on the miscibility of polymer blends were studied by means of Monte Carlo simulations. Using the bond fluctuation model on a simple cubic lattice, we were able to simulate symmetric linear/linear and-for the first time-star/star blends with a moderate number of arms. The simulations were made at a volume fraction of occupied lattice sites phi = 0.5, which corresponds to dense polymer mixtures for this algorithm. In particular, we studied star/star blends with 4, 8, and 12 arms and the respective linear blends, all having the same total number of units equal to 121. The critical points for the different blends indicated that the miscibility increased greatly when the number of arms f was increased. Our results are in agreement with recent analytical findings.