Heat oven to 400°F. In medium bowl, mash cheese with fork. Stir in chives, onions and lemon peel until well mixed.
On lightly floured surface, unfold pastry sheet; sprinkle lightly with flour. Roll pastry into 12-inch square. Cut pastry into 4 rows by 4 rows to make 16 squares. Spoon cheese mixture onto center of each square (about 1 rounded teaspoon each).
Moisten edges of 1 square with fingertip dipped in water. Fold square over filling to form a triangle, gently pressing to remove air pockets around filling and pressing edges of pastry together. Use tines of fork to crimp and seal edges of turnover. Repeat with remaining squares. Using spatula, make edges of turnovers even if necessary; place on ungreased cookie sheet.
Bake 10 to 15 minutes or until puffed and golden all over. Remove from cookie sheet to cooling rack; cool 2 to 3 minutes before serving.