Remove any membranes and excess fat from the fillet, rinse, dry with a paper towel, and cut into medium-sized cubes. Finely chop the onion and carrot, fry in sunflower oil, then add the chicken fillet. Season with salt and pepper to taste. Simmer for 30 minutes over low heat.
Chill the meat and pour it into a blender container.
Grind at high speed until a soft puree forms.
Transfer the puree to a container with a lid, add the softened butter, and mix well.
Close the container with a lid and place the pâté in the refrigerator for 1.5 hours.