We study a model of competitive information design in an oligopoly search market with heterogeneous consumer search costs. A unique class of equilibria—upper-censorship equilibria—emerges under intense competition. In equilibrium, firms balance competitive pressure with local monopoly power granted by search frictions. Notably, firms disclose only partial information even as the number of firms approaches infinity. The maximal informativeness of equilibrium decreases under first-order shifts in the search cost distribution, but varies non- monotonically under mean-preserving spreads. Instead, informativeness increases in the evenness of the search cost distribution, measured by minc H(c)/c. Finally, the model nests two canonical benchmarks as limiting cases: it converges to full disclosure as search frictions vanish and to no disclosure when search costs become homogeneous.