Combine chicken cubes and hot sauce in medium bowl and toss to coat well. Sprinkle with salt and pepper and toss again. Whisk chicken broth, peanut butter, and tomato paste in another medium bowl to blend.
Melt butter in large pot over medium-high heat. Add chopped onion and zucchini; sauté until tender, about 8 minutes. Add chicken and sauté until no longer pink on outside, about 3 minutes. Sprinkle with flour and cook 1 minute, stirring occasionally.
Add broth mixture and tomatoes to pot. Simmer until chicken is cooked through and flavors blend, about 5 minutes. Season soup to taste with salt and pepper. Serve.