We develop a rational inattention theory of echo chambers, where players allocate limited attention across biased primary sources and other players to gather information about an uncertain state. The resulting Poisson attention network transmits information from the primary source to a player either directly or indirectly through other players. Rational inattention creates heterogeneous information demands among players who are biased toward different decisions. In an echo-chamber equilibrium, each player focuses on his own-biased source and like-minded friends, who attend to the same primary source as his and can serve as secondary sources if the attention channel from the primary source to him is disrupted. We establish conditions for the emergence of echo-chamber equilibria, characterize the attention networks within echo chambers, and offer insights for designing and regulating information platforms.