How to cook extremely soft chicken?
That chicken has been "velveted". The technique is to briefly marinate the chicken chunks in a mixture of egg whites and cornstarch. The result is delicious, very soft chicken. It's a simple technique, great for stir-fried dishes and soups. There are several variations, so here are a bunch of them.

The simplest is to mix 1 Tablespoon of cornstarch into 1 egg white. Marinate thin slices of chicken (breast meat is most commonly used) in the mixture for 30 minutes. Drain the chicken by just letting the marinade slip through your fingers. Now just treat the chicken however you care to cook it; stir-fried, deep-fried or poached are all commonly seen. For something so simple, the result is really quite dramatic.