Combine the first 3 ingredients in a medium saucepan. Bring to a boil; cook 3 minutes. Cover, reduce heat, and simmer 8 minutes or until tender.
While barley cooks, heat the oil in a large nonstick skillet over medium-high heat; add artichokes and garlic. Sauté 3 minutes, stirring frequently.
Stir pesto, lemon juice, and chickpeas into the cooked barley. Serve artichoke mixture over barley; top with cheese.