Preheat grill to medium-high (if using a charcoal grill, coals are ready when you can hold your hand 5 inches above grate for just 3 to 4 seconds). Stir together 2 minced garlic cloves, the marjoram, 2 teaspoons oil, and 1/2 teaspoon salt in a small bowl; season with pepper. Place chicken in a shallow dish, and coat both sides with garlic mixture. Let stand at room temperature about 15 minutes, or up to overnight in the refrigerator.
Toss bell peppers with remaining garlic and 1 teaspoon oil in a medium bowl. Grill peppers, turning, until tender and blackened in places, about 15 minutes. Remove peppers from grill, and return to the bowl. Add 1 tablespoon vinegar; toss to combine. Set aside.
Cover potatoes with 2 inches cold water in a medium saucepan; bring to a boil. Reduce heat; simmer until just tender, 15 to 20 minutes. Drain; return to dry saucepan until ready to use.
Grill the chicken, turning halfway through, until browned and cooked through, about 10 minutes. Meanwhile, slice potatoes into 1/4-inch-thick rounds; sprinkle with remaining 1/4 teaspoon salt. Remove chicken from grill, and arrange on a serving platter with peppers and potatoes. Drizzle with remaining 1 teaspoon vinegar and oil, if desired. Garnish with marjoram sprigs; serve immediately.