Purchase several fresh chayote fruits in fall, even if they have been in cold storage and are wrapped in plastic. Unwrap them once you get home if they were encased in plastic.
Store whole chayotes in a cool, dark place such as a garage or back porch cupboard. The almond-sized chayote seeds inside the fruits will sprout, emerge and lengthen in the dark. By February, the seedling will be about 6 inches long.
Fill the 5-gallon container to within several inches of the top with thoroughly moistened potting soil. Scoop out a chayote-sized area in the center and plant the entire sprouted fruit, the tip barely showing.
Water the chayote pot thoroughly and place it in a sunny window until temperatures outside are warm. Keep soil evenly moist but not soggy.
Place the pot outdoors when temperatures are warm, adjacent to the fence or trellis that will provide support. Water regularly, thoroughly saturating the soil. You may water once or twice daily during hot weather, because roots are limited to moisture available to them in the container.
Mulch the chayote soil with several inches of mulch to conserve moisture. Tend the vine all summer; it will grow to 30 feet or more before blossoming or setting fruit. Vines will bloom in August or September and be covered with chayotes by September or October.
Harvest fruits when pickle size, sliced-cucumber size or 1-pound-pear size. Vines will die back after the first frost, but fruits won’t be damaged until the first hard frost. Protect the dormant roots by storing the pot in a cool -- not frosty -- garage or basement until spring. Water the pot lightly every month or so.