Postgresql Chained Slaves and Slave Promotion
You should be able to use recovery_target_timeline='latest' in your recovery.conf, as noted in the recovery target settings documentation

If you are on PostgreSQL 9.1 or 9.2 and using streaming replication, you'll need to have a WAL archive set up as well, if you want to have this continue automatically after failover, or as @amacvar mentioned, copy the necessary WAL segments over so that the replicas can continue streaming along the newer timelines.

In 9.3 and later, this happens without needing an additional WAL archive, because the timeline switch is now included in the replication stream. Michael Paquier details this behavior in his blog post timeline switch of slave node without archives