This circuit is designed around the MCP73837 chip. There are a couple different versions of this chip which allows the same PCB have a charge cut off voltage of 4.2V for normal lithium batteries and 4.35V for high capacity lithium batteries.

4.20V – MCP73837-NVI/UN
4.35V – MCP73837-FCI/UN

It charges via USB at a rate of 500mA or an external power supply rated at 5-6V at 1A. I would use a power supply at a rating of at least 1.2A for this charger.

Files (Eagle V6)

PCB V1.1
Schematic V1.1

PCB V1.2
Schematic V1.2

PCB Change Log

Bill of Materials

Name:            MFG P/N:               Mouser P/N:             QTY:
U1               MCP73837-NVI/UN        579-MCP73837-NVI/UN     1
U1               MCP73837-FCI/UN        579-MCP73837-FCI/UN     1
U2               BAW101,215             771-BAW101215           1
R1, R2, R3, R4   CRCW08051K00FKEA       71-CRCW08051K00FKEA     4
R5               CRCW080510K0FKEB       71-CRCW080510K0FKEB     1
C1, C2, C3       GRM21BC81E475KA12L     81-GRM21BC81E475KA12    3
LED1,2,3         598-8170-107F          645-598-8170-107F       3
J1               KLDX-0202-AP-LT        806-KLDX-0202-AP-LT     1
J2               54819-0572             538-54819-0572          1
J3               47346-0001             538-47346-0001          1
J4               47346-0001             538-47346-0001           1

Bill of Material on Mouser