Combine first 3 ingredients in a medium saucepan. Bring to a boil; cook 3 minutes. Cover, reduce heat, and simmer 8 minutes or until barley is tender and liquid is absorbed. Stir in pesto and chickpeas; cook 1 minute or until thoroughly heated. Stir in lemon juice.
While the barley cooks, heat the oil in a large nonstick skillet over medium-high heat. Add garlic and artichokes; sauté 3 minutes or until lightly browned.
Place 1 cup barley mixture into each of 4 bowls, and then top each serving with 1/4 cup artichoke mixture. Sprinkle each serving with 2 tablespoons of cheese.