Heat the olive oil in a saucepan over medium heat. Add the peppers and the onions. Fry for about 5 minutes until they start to brown and soften. Add tomatoes and garlic and cook for an additional 5 minutes.
Add the water, chicken stock, coarse salt, and pepper. Bring to a boil, reduce heat to simmer, cover, and cook for about 20 minutes.
In the meantime, mash the goatcheese, chives, and basil in a bowl until mixed. Divide the mixture into 12 portions and roll each into a small ball. Refrigerate until needed.
When the soup is cooked, puree it in a blender and strain.
Reheat soup if necessary. Salt to taste. Divide soup among serving bowls. Place 3 cheese balls in each bowl.