Place chicken in a slow cooker, and season with salt and pepper. With the exception of zucchini, add all remaining ingredients. Mix well.
Cover and cook on high for 3 - 4 hours, or on low for 7 - 8 hours, until chicken is fully cooked and veggies are softened.
Meanwhile, using a spiral vegetable slicer, cut zucchini into spaghetti-like noodles. (If you don’t have a spiral veggie slicer, peel zucchini into super-thin strips, rotating the zucchini after each strip.) Roughly chop for shorter noodles.
If cooking at high heat, decrease to low. Remove and discard bay leaves.
Transfer chicken to a large bowl. Shred chicken with two forks -- one to hold the chicken in place and the other to scrape across and shred it. Return to the slow cooker.
Stir in zucchini noodles, re-cover, and cook for 10 minutes, or until noodles have slightly softened.
Add more salt and pepper as needed.