Why do people spread rumors? This paper studies the transmission of possibly false information---by rational agents who seek the truth. Unbiased agents earn payoffs when a collective decision is correct in that it matches the true state of the world, which is initially unknown. One agent learns the underlying state and chooses whether to send a true or false message to her friends and neighbors who then decide whether or not to transmit it further. The papers hows how a social network can serve as a filter. Agents block messages from parts of the network that contain many biased agents; the messages that circulate may be incorrect but sufficiently informative as to the correct decision.