Combine the chilies with the onion, cilantro, agave, ½ teaspoon salt, and ¼ teaspoon pepper. Set aside.
Divide the ground chuck into 4 equal portions and shape into patties about ¾ inch thick. Make an indentation with your thumb in the middle of the burger patties. Brush both sides of the patties lightly with oil and season with salt and pepper. Let sit at room temperature while the grill heats.
Prepare a grill for direct and indirect heat and per-heat to medium-high. Oil the grates well. Grill on one side over direct heat with the lid closed for 4 minutes. Flip and grill with the lid closed for another 2 minutes. Move the patties to the indirect side of the grill. Top each patty with a slice of cheese. Close the lid and grill for another 1 ½ - 2 minutes or until the cheese is fully melted.
If desired, brush the cut sides of the burger buns with oil and toast over the direct side of the grill for 1-2 minutes.
Place one patty on the bottom of each bun, top with the burger, and then spoon on the green chili salsa.