Chayote squash is tough when raw. However, when it is cooked it tastes similar to a summer squash.
When buying chayote look for firm but smooth skin. The squash will certainly have a furrow like texture but it should not be overly so. The skin should also be bright as well. If you would like to store it, place it in a plastic bag and put it in the fridge.
Chayote can be fried for a great snack. You can also use it in a salad. If added to a salad make sure you soften it with lemon juice. Chayote also makes a great soup or stir-fry.