First, you need to poach your chicken breasts.
Turn your slow cooker up to high.
Spray your slow cooker with cooking spray.
Pour chicken broth into your slow cooker. You can use water instead of chicken broth but I find the flavor of the chicken is better if poached in chicken broth. My husband can't tell the difference. The decision is yours.
Place chicken breasts side by side, on the bottom of your slow cooker.
Cook covered for 1 ½ - 2 hours, or until chicken is done.
Using a thermometer, check your chicken near the end of cooking to avoid dry or overcooked chicken.
Remove the chicken when it reaches 165 degrees. Set chicken aside to rest and cool down.
Remove chicken from slow cooker into a medium sized bowl and shred with claws, two forks, your fingers or use a hand mixer on low speed.
These claws are terrific and make shredding so much easier. If you have never seen a pair, check them out. Meat Shredder Claws Cheap and the exact pair I started with. If you use the tool frequently then I suggest a stronger and more comfortable pair. These Meat Claws are stainless steel, more expensive with more comfortable handles.
Allow chicken to cool, usually about 15 minutes.
Combine shredded chicken, celery, onions, peppers, salt, pepper, mayonnaise, and anything else you want to include, in a large bowl.
Stir until well blended.
Cover and chill at least 4 hours before serving.