Heat a large Dutch oven over medium-high heat. Once hot, add the oil and heat it up for 30 seconds. Add the chopped onions and stir, sautéing them for 2 to 3 minutes until they're soft. Add the chopped bell peppers and garlic cloves, and sauté for 5 more minutes, until the peppers are soft.
When the veggies are soft, add the paprika, caraway seeds, salt, and pepper to the pot. Stir to toast the spices for 1 minute.
Add the chicken pieces to the pot and stir. Cook the chicken down for 3 minutes, until the outside of the chicken pieces looks white. You'll cook the chicken fully next.
Add the tomatoes, including their juices, and the chicken broth to the pot, then stir to combine everything.
Cook:
Bring the mixture to a simmer, reduce the heat to low, and cover the pot. Simmer for 30 to 45 minutes, opening the lid a few times to stir. In the last 10 minutes of cooking, check to see how much liquid is left. If you like your stews more soupy, add 1 to 2 cups of additional broth, stir, and bring to a simmer.
Serve:
Serve as is or over a serving of cooked rice.
Notes
Swap caraway seeds for fennel seeds or ground fennel.
Traditional chicken goulash is quite thick, but some people prefer theirs to have a soup-like consistency. I recommend buying a 32-ounce size of chicken broth and adding 1 to 2 cups towards the end of the cooking time.
Short on time? Swap the onions and peppers for 2 16-ounce bags of fajita mix (frozen).