Add the chicken, onions, peppers, about ⅔ of the salsa, and salt to a 6-quart slow cooker, stirring to combine.
Cover and cook on high for 4 hours or low for 6, or until the chicken and vegetables are very tender.
Uncover and remove the chicken to a cutting board. Shred with two forks or cut into pieces.
If there is a lot of liquid in the slow cooker you can drain some off or leave it all in, depending on whether you want a drier or saucier consistency.
Add back the chicken, the remaining salsa, and lime juice, stirring everything together. Taste and add additional salt, lime juice or salsa if you like.