The chicken and sauce you're describing is a Cantonese dish. It's pretty easy to make the ginger-green onion sauce at home. Chop up 2 or 3 green onion stalks, grate young ginger (available at 99 Ranch) until you have about 3 tablespoons and put together in a heat-proof bowl. Heat up a couple tablespoons of corn oil in a pan, pour the oil over the chopped onion and ginger mixture. Stir in some salt to taste, and if you have it, a pinch of powdered ginger. Dip poached chicken into the sauce.
I've made this ginger-onion sauce with bottled minced ginger too. You can adjust everything to taste.
Sam Woo BBQ gives a tiny little plastic container of the ginger-onion sauce when you buy their chicken. Better to make a generous amount of fresh sauce at home!