Grate the zucchini and salt them. Let stand for 30 minutes in a colander. Squeeze the zucchini dry with your hands or wring it out in a towel.
Peel and chop the garlic fine, chop fine about 1 tablespoonful of the chives, and grate the zest from the lemons.
In a large bowl, combine the zucchini with the garlic, chives, lemon zest, the potato starch, and the egg, lightly beaten. Heat the olive oil in a nonstick sauté pan over medium heat. For each fritter, pour a generous tablespoonful of the zucchini batter into the pan. They will look like little pancakes. Turn them over after about 3 minutes, or when golden. Cook 2. minutes more on the other side. Drain on paper towels.