Chop onions and chayote. Cook in the butter until partly cooked. Add the cheese, salt, and pepper; mix well. Pour the mixture into the unbaked pie shell. Beat the two eggs until fluffy and pour over the chayote mixture. Bake in a 350 degree F. oven until eggs are done inside and browned. Cut into wedges and serve warm.
Note: The chayote can also be made into an omelet by using the above ingredients without the pie shell.