Salt and pepper the chicken breasts. Set aside.
Place the garlic, gingerroot, and peanut oil in a large skillet over medium-high heat and cook for 1–2 minutes, until tender.
Stir in the chicken and cook while stirring 5–8 minutes, until browned and no longer pink.
Place the cooked chicken in the slow cooker. Add the remaining ingredients to slow cooker except vegetables. Stir to combine. Cook on low for 6 hours.
Add vegetables including jalapeno and let cook another 30 minutes, until they soften. garnish with sliced green onions and lime wedges.