In a large Dutch oven, heat the cooking oil to medium.
Add onions and cook about 8 minutes.
Add garlic, stir, and cook for an additional 1 minute.
Add tomatoes and chicken. Bring to a simmer at medium-high. Simmer for 8 minutes.
Stir in the green beans, zucchini, yellow squash, oregano, thyme, red pepper flakes, salt, and dried basil (if using fresh herbs, do not add them yet).
Simmer, stirring occasionally, until vegetables are tender and the chicken is cooked through with no pink remaining in center. This timing will vary depending on your chicken sizes. Start checking the temp in the center of the larger pieces after about 15 minutes and go from there. Internal chicken temp should be at least 175 for the best flavor. (above 190 may start to get tough or dry)
If using fresh herbs, stir them in just before serving.