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Put chicken in slow cooker.
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In a mixing bowl, whisk together brown sugar, vinegar, lemon-lime soda, garlic, soy sauce, and pepper. Pour over the chicken in the slow cooker.
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Cook on low for 6 hours or high 3-4 hours, until the chicken is practically falling apart.
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Remove chicken and shred.
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Pour the liquid into a saucepan.
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In a small bowl, whisk together cornstarch and water until no lumps remain. Pour into saucepan and whisk to combine. Bring to a simmer and let it go for about 3 minutes or until it thickens slightly. Stir in chicken.
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Serve hot.