Preheat your grill for 2-zone cooking at 375°F.
Lightly coat chicken thighs with oil. Season generously with salt, pepper, garlic powder, and cayenne powder.
In a bowl or blender, combine all blue cheese sauce ingredients and mix until smooth. Refrigerate until ready to use.
Place chicken on the hot side of the grill and sear for 2–3 minutes per side.
Move chicken to the cooler side of the grill. Brush with buffalo sauce, close the lid, and cook until internal temperature reaches 165°F (about 10 more minutes).
Remove chicken and let rest, then slice into bite-sized cubes. Toss in additional buffalo sauce if desired.
Prepare crispy fries according to package instructions or your preferred method.
Spread fries onto a large serving platter and melt shredded cheese over the top.
Top fries with buffalo chicken, drizzle generously with blue cheese sauce, add more buffalo sauce, and garnish with blue cheese crumbles and chopped chives.
Serve Buffalo Chicken Fries immediately while hot and melty.