We argue that chaotic power-law interacting systems have emergent limits on information propagation, analogous to relativistic light cones, which depend on the spatial dimension d and the exponent a governing the decay of interactions. Using the dephasing nature of quantum chaos, we map the problem to a stochastic model with a known phase diagram. A linear light cone results for alpha >= d + 1/2. We also provide a Levy flight (long-range random walk) interpretation of the results and show consistent numerical data for 1D long-range spin models with 200 sites.