I opened a cheap USB single-cell lithium-ion battery charger, but can't figure what the Q1 is. It only says 'CR' on the surface. When charging, I measure about 0.7 V between its pins 1 and 2 (those on the same side), so maybe it plays a role of a diode that drops the voltage from 5 V to 4.3 V, which is approximately the full charge voltage of the 3.7 lithium cell.
I can also measure with a multimeter in diode mode that it behaves similarly to a PNP: it shows about 0.7 V between pins 3-1 and 3-2, hinting that pin 3 is the base. But then it shouldn't create a voltage drop between emitter and collector when active. Or maybe it's just a custom component?