Heat olive oil in a large Dutch oven over medium-high heat. Add half of chicken to pan; cook 5 minutes, browning on all sides. Remove chicken from pan. Repeat procedure with remaining chicken.
Add onion to pan; sauté for 3 minutes or until tender. Add ginger and next 6 ingredients (through garlic); sauté for 30 seconds or until fragrant. Stir in broth, scraping pan to loosen browned bits. Return chicken to pan; bring to a simmer. Cover, reduce heat, and simmer 1 hour or until chicken is tender.
Remove chicken from pan with a slotted spoon; cool slightly. Cut chicken into bite-sized pieces. Add chicken, chickpeas, and apricots to pan. Cover and simmer 10 minutes or until thoroughly heated.