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. As with bacon or pancetta—or any other meat, really—throwing it on a plate and placing it in the freezer for about 15 minutes will help it firm up and make it easier to slice precisely.
Muscle Grain Matters
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.
Chicken breast is a little different than most cuts of meat you'll encounter since the grain isn't uniform across the entire chicken breast half. Here's a rough diagram of the orientation of the grain on a boneless, skinless chicken breast:
Chicken is also a little different from other meats in that you want to slice not quite 100 percent against the grain, because it can end up almost too tender if you do. But you still want to cut at a sharp bias against it.
How to Slice Chicken Breast for Stir-Fries
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.
How to Julienne Chicken Breast for Stir-Fries
If you want slivers of chicken breast to toss into a stir-fry, you cut the chicken breast as you would for slices, but then you take those same slices, stack a few at a time, and slice them lengthwise.
Only stack as many slices on top of each other as you feel comfortable slicing. The goal is to produce relatively uniform matchstick-lengths of chicken breast.
How to Dice Chicken Breast for Stir-Fries
If you're making a recipe that calls for diced chicken breast, as in my Sichuan kung pao chicken, you'll want to start by slicing the chicken into wider strips.
Then cut each of those wider strips crosswise into cubes. If you want to cut up smaller cubes, take each of the wider strips and slice it in half lengthwise, then cut the resulting strips crosswise.
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.