Heat a large pot over medium heat and add olive oil.
Add diced onions, carrots, and celery and sauté for 3-5 minutes, stirring often, until onion becomes translucent.
Add garlic, salt, pepper, and thyme and saute for 2 more minutes, stirring often.
Add chicken broth and cover until broth mixture comes to a boil.
Add chicken breasts and cover and cook for 12-15 minutes until cooked all the way through. Remove chicken breasts and place on a cutting board.
Add frozen peas and corn to the pot, cover and cook for 8 minutes.
Meanwhile, chop the chicken into bite sized pieces. Add chopped chicken back to the pot after the corn and peas are done cooking (they should be tender).
In a small bowl, whisk together milk and corn starch until no clumps remain. Add mixture to the pot while stirring until it thickens.
Remove from heat and serve! I like to serve with crackers or toasted bread on the side.