Rinse peas; drain. In a large saucepan, stir together peas, chicken broth, water, bay leaf, thyme or marjoram, and pepper. Bring to boiling; reduce heat. Cover and simmer for 1 hour, stirring occasionally.
Stir in carrots, potatoes, ham, celery, and onion. Return to boiling; reduce heat. Cover and simmer about 20 minutes more or until the vegetables are tender. Discard bay leaf. Makes 4 main-dish servings.