In this paper we are concerned with a scenario in which multiple messages (K) are concurrently flooding a dense wireless network. Rather than using standard packet switching we assume that the nodes relay cooperatively the messages, if they are able to decode them. Our objective is to propose and analyze a scheme that exploits the alignment of interference that opportunistically arises in the relay process. More specifically, each receiver observes the K messages over D dimensions through an MIMO random channel. For each message, there exists an MIMO channel matrix that is associated with the interference. The key idea is to use the spatial occurrence of MIMO interference matrices that have a high condition number to design good beamformers to decode the messages. We refer to this effect as opportunistic interference alignment. We show that this scheme can result in successful broadcast.