Fill peat pots with a good-quality potting mix containing peat moss and perlite, or make your own mix by combining equal measures of coarse sand, coconut coir and aged compost. Pour 1/8 cup of water to each filled pot to moisten the mix thoroughly.
Put one alligator pepper seed in each pot. Press the seed into the mix to 1/4-inch deep. Pinch the hole above the seed closed and press the potting mix firmly around the seed.
Put the peat pots in a nursery tray that will hold the pots erect and keep them from falling over. Cover the pots and tray with plastic wrap to hold in heat and moisture.
Place the covered tray where seeds get at least six hours of bright light daily. Put a propagation mat set for 75 degrees Fahrenheit under the tray.
Keep the mix in the pots evenly moist, adding water as necessary to keep the mix from becoming dry. Remove the plastic wrap once seeds sprout, usually within 15 to 20 days after planting. Continue to keep the mix moist.
Transplant the seedling to a 4-inch pot when it has several sets of true leaves and is 2 to 3 inches tall. Use a mix similar to the one used for germination. Place it in an area with partial sun.
Repot the plant as the roots fill the pot in which it is growing. Put it in a 1-gallon pot and gradually get the plant used to more sun. Keep the potting mix moist.
Put well-rooted larger alligator pepper plants into tubs, half-barrels or 10-gallon containers, since they develop rhizomes and need root room. Watch for the appearance of pink lily-like flowers growing from the rhizomes after about a year.
Maintain the plants, keeping the soil moist at all times and keeping the plants from frost, since a plant can produce seeds for over 10 years if well-cared for.
Transfer established plants from containers into a garden bed with well-drained, highly organic soil in a sunny, open area. Wait until air temperatures are 75 degrees Fahrenheit or more during the day and above 50 degrees F at night.
Space plants 48 inches apart to give room for growth. Dig a hole slightly larger than the rootball. Put the plant from the container into the hole and backfill, tamping the soil firmly. Water the plants immediately after planting and keep the soil evenly moist thereafter.
Watch for flowering and fruiting, and harvest the alligator pepper fruits once they are red.