The term "fry" is a little confusing in this context. What, exactly, did you try and do? Skinless, boneless chicken breast in a dry pan with no oil, some oil, or lots of oil? Seasoning or no seasoning? Did the pan start hot? Or did it start cold?
The more you can tell us about your "learning experience," the more specific we/I can be.
Psycho chef covered two very important items. Let's see if we can't expand a little.
A chicken breast meat is mostly protein and water. When the breast hits the bottom of the pan -- even if the pan is full of oil, some of the water starts to move through the breast away from the heat; and, the protein molecules -- and some of the meat juices -- begin to undergo a chemical change which converts them to sugar like molecules. The proteins and juices brown and crystallize in something often referred to as the Maillard reaction. During the period of crystallization, the meat will stick to the pan. After the change, the meat will "release." This doesn't necessarily mean it will slide off easily, but it will move more easily. When it does move, the meat will leave a little of the crystallized juices behind in a little ring on the pan. The juices left behind are called fond.
In the meantime, it sounds like you're having trouble with the pan. If you're "sauteeing" or pan-frying (two similar but not identical techniques), you need to preheat the pan before putting the oil in it. After the pan is hot, add the oil. Then let the oil come to temp before adding the meat. In this way you maximize the lubricating effect of the oil and hasten the Maillard reaction.
As the oil heats it will become thinner and less viscuous, and move around the pan more easily. It will also heat the air immediately above it which will seem to shimmer. These are two signs the oil is ready: 1) A little bit moves around the pan very easily, like water. 2) The oil shimmers.
If the oil is too hot it will smoke. That's a bad thing. If you see dark smoke coming off your oil, let the pan cool down, throw the oil away, and start over with new oil. Oil which has been overheated will not lubricate, will taste bad, will color your food, and is actually very unhealthy. To help prevent this from happening, lift the pan off the flame for a few seconds before adding the oil, then put it back.
Breading your chicken will help keep it from sticking too. The breading acts like ball bearings -- but it's not necessary. Better for most applications, though. A different cooking lesson perhaps.
As psycho implied, splattering is almost entirely an effect of water in the pan. The hot oil floats on the water, the water boils and forms steam bubbles, the bubbles rise to the surface and burst, kicking hot oil everywhere. Most meats and foods bring some moisture to the oil and splatter happens -- which is why you shouldn't pan-fry naked.
So ... hot pan, hot oil (you don't need much), dry chicken, wear underwear, and let the chicken brown before you try and move it.