The first step to great food is great knife skills. Check out more Knife Skills this way!
Even if you have the very best chef's knife and that knife is carefully sharpened and honed after each use, chicken can still be a bit slippery to slice. Throw it on a plate and place it in the freezer for about 15 minutes to help it firm up.
All muscle matter has a grain to it. The muscle fibers align in the direction that they contract. The orientation of your knife to this grain will determine the length of the muscle fibers in an individual slice of meat, which in turn will have a profound effect on how tender or tough that meat is.
With chicken, you want to slice not quite 100 percent against the grain (it can end up almost too tender if you do), but you want to cut at a sharp bias against it.
For slices, hold the chicken breast with your non-knife hand, curling your fingertips under your knuckles (so you don't slice them off!), and slice the chicken with long, even strokes into slices about 1/4-inch thick.
For julienne, take those same slices, stack a few at a time, and slice them lengthwise into matchsticks.
If a recipe calls for dicing, start by slicing the chicken into wider strips.
Working one slice at a time, slice it lengthwise into long strips...
...then cut crosswise into dice.
The chicken is now ready to cook in any number of Chinese recipes, whether they involve velveting (coating with egg white and corn starch, like in this Stir-Fried Velvet Chicken with Snap Peas and Lemon-Ginger Sauce), simple marinating, like in this Easy Stir-Fried Chicken With Ginger and Scallions, or this Kung Pao Chicken, or this Kimchi Chicken and Cabbage Stir-Fry, or just cooked as-is, like in this Chicken Red Curry Stir-Fry with Green Beans.