Melt the butter in a large stockpot over medium-low heat. Add the onion and ½ teaspoon of the salt. Cook, stirring often, until the onion is soft and translucent, about 10 minutes.
Add the broth and bring to a boil over high heat. Stir in the pasta, frozen vegetables, and tomatoes. Cook until the pasta is done, about 7 minutes.
Stir in the chicken, Parmesan, lemon juice, remaining salt, pepper, and chives, if using. Cook 1 more minute to heat through, remove from heat, and serve.