From our June 18, 2012 newsletter:
So, what are pea shoots? Pea shoots are the choice leaves and tendrils of pea plants. Shoots are typically harvested from snow pea vines, although they can be from any type of garden pea. All parts of the pea plant are edible. When they are young, the pea shoots are both tender, but crisp and tasty, and they taste basically just like peas. The same goes for those curling, clinging tendrils the pea plants use to hold on to supports. You’ve probably seen them on plates in Asian restaurants and trendy establishments. Pea shoots and tendrils may look exotic or sophisticated, but even gardeners who can’t grow peas to maturity can grow pea shoots and tendrils.Pea Shoots are delicate things. They only keep for a couple of days at max, so you'll want to use them quickly while they are fresh.
Store them if you must by putting them in a brown paper bag in the vegetable crisper in your refrigerator. The bag will help to regulate moisture. An alternative would be to simply wrap them in dry paper towels and put them in the crisper.