SQL Dude-467553 (4/30/2010)
I think this question really makes me think. I thought the log backup chain was broken after a full backup based on this I read on MSDN"If a log backup becomes missing or damaged, start a new log chain by creating a full or differential database backup and then backing up the transaction log to start a new log chain. We recommend that you retain transaction logs backups that come before a missing log backup, in case you ever want to restore the database to a point in time within those backups. For information about how to help protect your backups, see Security Considerations for Backup and Restore (SQL Server)."
If a t-log backup becomes damaged or missing, yes, you need to start a new log chain by performing a full or differential backup. The key here is that the full and differential backups themselves don't BREAK a log chain.