Combine olive oil, orange juice, 1/8 teaspoon each salt and pepper in a medium bowl; add fennel. Toss to combine; cover and chill 1 hour.
In the meantime, heat grill or grill pan to medium-high. Season chicken with the remaining 1/4 teaspoon each salt and pepper, place on grill and cook for about 4–5 minutes on each side, or until cooked through. Set aside and keep warm.
Add orange sections and pomegranate seeds to fennel mixture; toss gently to combine. Top with almonds and mint. Serve salad with chicken breasts.