Place chicken pieces in a container; pour enough soy sauce on top to cover. Refrigerate and marinate for about 24 hours, the longer the better.

Heat a large pan over medium-high heat. Remove chicken from soy sauce and cook until crisp, 3 to 4 minutes per side. Remove chicken and let rest. Cook and stir onion in the pan until translucent, about 5 minutes.

Return chicken to the pan. Mix 1 cup cola with cornstarch in a small bowl and pour into the pan. Pour in enough of the remaining cola to cover the chicken. Bring to a boil, then lower heat and simmer, covered, until chicken is no longer pink in the center, about 45 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).

Pour some of the soy sauce marinade into the pan. Heat thoroughly, taste, and adjust seasoning if needed.