Mix the tuna, gluten free breadcrumbs, eggs, mayonnaise, and chives together in a bowl. Season with salt and pepper.
Divide the mixture into 8 and shape into patties. Cover and place in the fridge for 10 minutes.
Heat the oil in a large frying pan over a medium-high heat. Cook the burgers in batches for 2 minutes on each side, or until well browned and cooked through. Serve immediately, with gluten free buns if using