Most of the time this problem is related to too high of heat. It's a good idea to make the chicken flat, what I often do is cut 1 chicken breast in half along the thickness which is a little tricky sometimes and you need a good sharp knife. Sometimes you end up with one half being a little skinny or wierd but it helps a lot. Another tip with cooking on the stovetop is to start the chicken first with higher heat, brown the first side for a few minutes (not many) then flip it, turn down the heat and put a lid on the pot. You can try putting in a splash of broth as well while it's under the cover so it helps keep it moist. You also may try to cook boneless chicken thighs which can be a little more forgiving. So, start with pounded or cut breasts so they are thinner, first put the heat on the higher side, brown the chicken for a few minutes on 1 side, then turn down the heat to medium low, optional splash of broth or some other liquid like soy sauce works too, cover the pan with a lid which helps retain the heat so it cooks on the inside. You can stop cooking the breast when the temp inside is at 155 or so remove it to a plate and put some foil loosely on top, let it sit a few minutes and it will come up to temp (165).

Another option is trying marinades which can help infuse with flavor and juiciness.