I'm using the MCP73812 for battery charging. 

I've decided to keep the battery charging on the blimp's gondola itself rather than dealing with pulling the battery on and off each time. I dislikeJST-style battery connectors.

After leaving the battery on charge to test the circuit overnight, I discovered that this morning, the 1-cell 3.7V Li-ion battery was at 2.8V. !!!!!! 

Update: while charging, the rest of the circuit was on, so the motor was on all night. In the next rev, I've fixed that.

This is the circuit (*.sch in docs) I'm using.

Good article describing Li-ion charging.