Heat a large soup pot over medium heat. Add oil, onion, carrot, thyme and rosemary. Cook until onions are softened and starting to brown, about 5 minutes.
Stir in garlic and Swiss chard and cook until aromatic, about 30 seconds.
Add stock, tomatoes and acini de pepe; bring to a simmer.
Season with salt and pepper and cook until ancini de pepe is al dente, about 10 minutes).
Taste and adjust seasoning. Divide between 4 bowls and sprinkle with basil.