In a small mixing bowl, combine the sour cream, mayonnaise, garlic powder, ⅛ teaspoon salt, and ½ teaspoon pepper. Mix until smooth. Stir in the blue cheese crumbles. Cover and refrigerate until serving time. Can be made a day ahead.
Prepare the grill for direct heat and heat to medium-high.
Divide ground chuck into 6 equal portions. Form each portion into patties and make a depression in the center of each patty with your thumb. Brush the patties with oil and season with salt and pepper.
Grill the burgers for 4 minutes with the lid closed. Flip the burgers and cook, with the lid closed, for another 3-4 minutes for medium-rare. Grill the hamburger buns until toasted, if desired.
Spread a little mayonnaise on each cut side of the buns. On the bottom buns, place some lettuce, top with a tomato slice, a burger patty, and dollop with the blue cheese sauce.