Peter T Miller writes:
Like other simple, single-cell lithium-ion battery chargers, Microchip’s MCP73812 provides no means of indicating the charging status. You can remedy this situation by adding four components (Figure 1). Add one more LED, and you also get a charging-complete indication. This two-LED configuration has the added benefit that one of the LEDs is always on, providing an indication that the charger is powered.
Add charging status to simple lithium-ion charger - [Link]