AES-CBC with zero IV and a unique first block
If the IV is all zeroes, then you basically have ECB for the first block.  Basically you're proposing to use this first block's encryption as the IV for the second block.  You're implying that the first block will always be unique, but low entropy, which sounds like a counter or time stamp.  There are attacks when the IV is predictable, and while this is a step away from that, it may still be useful information for an attacker.