In a small bowl, whisk together the oil, lemon juice, soy sauce, honey, shallots, oregano, ½ teaspoon salt, and ¼ teaspoon pepper.
Place the ground beef in a large bowl and mix in 3 tablespoons of the vinaigrette. Form meat into 4 patties.
Heat grill to medium-high. Cook burgers to desired doneness, 5 to 6 minutes per side for medium-rare. (Or cook them in a skillet over medium-high heat.)
Spoon the remaining vinaigrette mixture over the burgers and serve with the potato chips, if desired.