Place the chicken breasts in the slow cooker in a single layer.
Pour the teriyaki sauce and soy sauce over the chicken, then sprinkle the pressed garlic evenly on top.
Top the chicken with the drained pineapple chunks.
Cook on high for 150–180 minutes (2.5–3 hours) or on low for 210–240 minutes (3.5–4 hours), until the chicken is cooked through and tender.
Remove the chicken to a cutting board, shred it with two forks, then return the shredded chicken to the slow cooker and stir to coat with the sauce.
Top with chopped green onions and serve warm.