Place the olive oil in a large saucepan and heat over medium-high heat until hot. Add chicken; cook and stir about five minutes or until chicken is browned. Add onion; cook and stir two minutes.
Add chicken stock, undrained tomatoes, cannellini beans, carrots, potato, salt and pepper. Bring to a boil, stirring to break up tomatoes. Reduce heat to low; cover and simmer for 15 minutes, stirring occasionally. Add green beans and cook for five minutes or until vegetables are tender.
Ladle soup into bowls, top each with one teaspoon pesto and sprinkle with parmesan cheese.