Bring water to a boil in a medium saucepan. Gradually add polenta, stirring constantly with a whisk. Reduce heat, and simmer 3 minutes, stirring frequently. Remove from heat; stir in butter. Cover and set aside.
While polenta cooks, heat oil in a large nonstick skillet over medium-high heat. Add onion and garlic; sauté for 3 minutes. Add lemon juice, cumin, black pepper, chickpeas, and tomatoes; bring to a boil. Reduce heat, and simmer 6 minutes. Stir in the green onions. Serve stew over polenta. Top with sour cream.