It sounds as if you are overcooking. How are you cooking the chicken breast?
Do not feel bad. It is very easy to overcook chicken breasts. You want to ensure that they are cooked thoroughly according to the US department of Agriculture but if you do so you end up with some fairly dry chicken breast.
How do you determine when the chicken breast is done?
I do it by feel. If you touch the chicken breast while cooking you will notice of change in the firmness as it cooks. Poke at it without piercing the skin and you will be able to observe how done the chicken breast is. With a little experimentation you should be able to find the right squishiness feeling, the breast should be firm but not too firm.
Personally I tend to try to under cook slightly but will remove the chicken from heat and tent it with aluminum foil while I prepare the rest of the plate. The slightly undercooked chicken continues to gently steam and by the time it is served we have one serious juicy chicken breast.
Try this:
We hedge our bets by marinating our chicken breast in advance.
Marinades are wonderful things that will add loads of flavor not to mention adding moisture to help keep things juicy.
In advance placed the chicken breasts into a plastic baggie along with the following ingredients. Toss in the fridge until you are ready to cook it. Feel free to improvise. Marinades can be a lot of fun and there is a lot of flexibility.
One tablespoon of olive oil
the juice of one half of one lemon
garlic to taste
ginger to taste
soy sauce perhaps
seasonings to taste
more or less of anything, wine is good too
dry or fresh herbs
or perhaps a vinegar to replace the lemon juice
As long as you have an oil and and acid (vinegar or lemon juice) it'll work out.
If you fry the breasts in a pan with a little bit of olive oil or butter it is very easy to overcook but it gives you a great opportunity to poke at the breast and observe the fine line between moist and juicy and dry.
The best bet is to brown over medium high, one or two minutes each side and "finish" in the oven. Try tenting with foil in the oven and before serving.
I hope this helps.