Rinse the zucchini and slice them with a vegetable peeler into long, thin ribbons. Peel the garlic and chop it finely. Rub the chicken fillet all over with salt and pepper. Toast the pine nuts in a dry pan until they turn light brown, then immediately set them aside on a small plate.
Heat a grill pan over high heat and grill the seasoned chicken fillet for six to eight minutes per side until fully cooked. Meanwhile, heat the olive oil in a large pan or wok over medium-high heat. Add the finely chopped garlic and sauté briefly. Add the zucchini ribbons and cook for a maximum of two minutes, so they retain a light bite.
Remove the pan with zucchini from the heat and stir in the green pesto until all the ribbons are evenly coated with sauce. Remove the cooked chicken fillet from the grill pan, let the meat rest briefly and then slice it with a sharp knife into diagonal slices.
Divide the warm zucchini linguine onto plates. Arrange the sliced chicken fillet neatly on top of the vegetables. Sprinkle the toasted pine nuts over everything and finally grate Parmesan cheese over the dish to taste.