Combine soy sauce, vegetable oil, dark brown sugar, Worcestershire sauce, Dijon mustard, garlic, chives, black pepper, and balsamic vinegar in a large dish or ziplock bag.
Add the flank steak to the marinade, cover, and refrigerate overnight or at least for all day.
Preheat the gas grill to high heat.
Remove steak from the marinade and grill for 2 minutes on each side over high heat.
Reduce heat to medium and continue cooking the steak for another 7-10 minutes, flipping halfway, until it reaches an internal temperature of 130°F for medium rare.
Remove steak from grill and rest on a cutting board, covered loosely with foil.
Simmer half of the remaining marinade in a saucepan over medium heat for 10 minutes to make a sauce.
Slice the steak against the grain and serve with a drizzle of the prepared sauce.