L-theanine is sometimes used in herbal medicine to help treat conditions including stress and insomnia. It can help people relax without increasing feelings of drowsiness. Chamomile tea may have similar effects and is also sometimes used to treat these same conditions, but this doesn't mean it contains L-theanine.
All teas aren't created equally -- only true teas, such as green, black and oolong tea, contain L-theanine. Chamomile tea is an herbal tea made from the flowers of the chamomile plant, while L-theanine is found in the Camellia sinensis plant, which is used to make true teas. You can also get L-theanine from a type of mushroom called Boletus badius or purchase it in supplement form.