In a medium mixing bowl, whisk together half of the soy sauce (1½ tbsp), half of the vinegar (1½ tbsp), and the coconut palm sugar or honey until combined.
Add the cubed chicken to the bowl and toss to coat with the marinade; refrigerate to marinate for 30 minutes.
Heat the olive oil in a large skillet over medium-low heat until shimmering.
Add the minced garlic and chopped ginger and cook, stirring, about 30 seconds until fragrant and the garlic is just golden; do not let it burn.
Add the marinated chicken with any remaining marinade from the bowl and cook, stirring occasionally, about 3 minutes to brown the pieces.
Stir in the red bell pepper strips, the remaining soy sauce (1½ tbsp), remaining vinegar (1½ tbsp), and the freshly ground black pepper; mix well.
Continue cooking for about 10 minutes, stirring occasionally, until the peppers are softened and the chicken is cooked through (no pink inside).
Serve the chicken hot over or alongside brown rice or quinoa if desired.