Combine peanut butter, water, lime juice, brown sugar, tamari (or soy sauce), fish sauce, hot sauce and garlic in a blender. Pulse until smooth.
Combine zucchini, cabbage, carrot and cilantro in a large bowl. Add 1 cup of the dressing (reserve the rest for another use) and toss to coat. Top the salad with chicken and peanuts. Serve immediately.
To make ahead: Refrigerate sauce (Step 1) for up to 3 days.