Heat 1 Tbsp. of oil in a small pot set over medium heat. Add the onion and ginger and cook until tender, about 4 minutes. Add the juice, water, sugar, vinegar, cumin, cayenne and 1 of the cubed plums. Bring to a simmer, and cook until the plum cubes are slightly falling apart and liquids are reduced and saucy, about 4 to 5 minutes. Spoon the mixture into a bowl. Stir in the other 2 cubed plums and mint or cilantro. Season with salt and pepper, cool to room temperature and then cover and refrigerate salsa until needed.
Preheat your barbecue or indoor grill to medium-high. Brush chicken with the 2 Tbsp. oil; season with salt and pepper. Lightly oil the bars of the grill. Grill the chicken 3 to 4 minutes per side, or until cooked through. Plate the chicken. Allow diners to top chicken with plum salsa, to taste.