Heat oil in a heavy-duty skillet or saucepan on medium-high heat. Set a candy thermometer in place.
While oil is heating, cut chicken breasts into cubes, then place in a food processor. Process chicken into a fine paste. Transfer processed chicken to a bowl. Combine salt, parsley, oregano, onion powder, and pepper, and sprinkle over chicken. Combine well.
Whisk eggs together in a small bowl. Combine the flour and salt and put it on a plate.
Measure chicken paste out with a cookie scoop and roll into 42 balls.
Roll ball in flour, then coat with egg, and then coat in flour again. Use your fingers to press the ball down to make a nugget.
Once oil reaches 350-365 F place as many nuggets as possible in the oil, and fry until the bottoms are golden, turn and fry until the other side is golden, about 4-5 minutes per side. Remove to a towel-lined plate (to catch any excess oil).