Preheat oven to 400 degrees.

Stir garlic into pesto container.  Transfer 1 tbs. of pesto mixture to small bowl and reserve. Transfer chicken into large roasting pan and rub 1/4 cup of pesto mixture over the outside of chicken and 1 tbs into the main cavity of chicken.  Put potatoes in a bowl and toss with the remaining pesto mixture.  Place potatoes in roasting pan along the side of the chicken.  Season chicken and potatoes with salt and pepper.

Roast chicken until thermometer inserted into the thickest part of the chicken thigh registers 180 degrees and potatoes are brown, about 1 hour and 20 minutes. 

Transfer chicken and potatoes to a platter.  Add broth and reserved 1 tbs of pesto mixture to the roasting pan.  Place pan over heat, bring to a boil, scraping up browned bits.  Reduce mixture for 1 minute.  Strain sauce before serving.

Serve chicken and potatoes with sauce.