Heat the oil in a large pot set over medium heat.
Sauté onions, carrots, celery, and chard stems until vegetables are onions are tender, about 5 minutes. Add garlic and cook for 2 more minutes.
Add the bay leaf, Italian seasoning, a few turns of fresh pepper, and a pinch of kosher salt.
Add the chicken, stock, tomatoes, drained and pureed beans, cream corn, lemon zest and juice, and Italian seasoning.
Bring to a boil and reduce heat to simmer for 30 minutes.
Remove the chicken thighs, and shred the chicken, discard the bones and skin.
Add the chicken back to the pot with the Swiss chard and peas.
Add the fresh dill if using; taste for seasoning, and It's ready to serve.