Preheat oven to 375 degrees. Heat olive oil in oven-proof stock pot or dutch oven on medium-high heat. Add carrots and onion and cook until onion is soft, about 10 minutes. Place pot in oven and bake until vegetables begin to brown, stirring occasionally 45 - 60 minutes.
Remove from oven, add garlic, thyme, marjoram, salt and chicken broth. Cover and simmer on stove top until carrots are very tender, about 30 minutes.
Transfer to blender and puree until smooth adding more chicken broth until desired consistency is attained. Ladle soup into warmed bowls and garnish with minced chive or green onions.
This is a great dairy-free soup but you can add a touch of cream at the end for added richness.