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Place the chicken pieces, bell peppers, onion, and pineapple chunks into the slow cooker.
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In a medium bowl, whisk together the pineapple juice, apple cider vinegar, ketchup, brown sugar, soy sauce, garlic, and ginger until the sugar is dissolved and the sauce is well combined.
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Pour the sauce over the ingredients in the slow cooker and stir to ensure everything is evenly coated.
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Cover the slow cooker and cook on low for 3 to 4 hours or on high for 1.5 to 2 hours, until the chicken is tender and cooked through.
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In a small bowl, whisk the cornstarch and cold water together until smooth to create a slurry.
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Stir the slurry into the slow cooker and cook on high for an additional 20 to 30 minutes until the sauce has thickened to your liking.
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Serve the chicken and vegetables warm over a bed of white or brown rice.