A lot of folks are fooled into a fall sense of security by the term "safety chain". They assume incorrectly that a safety chain eliminates the chance of kickback,rather than minimizes to the limits of common sense that a kickback will occur.
As mentioned above, use some common sense. Keep the upper part of the sprocket out of wood,if you are doing an upper cut use the bar rather than the nose to do the cutting. Avoid pinching by using your wedges in situations where the wood wants to close up on you.If you dont have any wedges, get some. Get the plastic kind,not steel that is used for splitting, and while you are waiting for your wedges to show up assuming you order online then make yourself some out some pieces of wood.
And above all else, if you havent invested in some proper safety equipement, get some yesterday.A woodsman helmet with a flip down shield can be your best friend when it comes to saving your noggin in a kickback situation, but dont forget a good pair of chaps.Although I will admit that I am one to leave the chaps in the truck many times, I never hesitate to slap a pair on in high risk areas like clearing brush,tangled wood,etc. Experience is your best tool in your arsenal against injuries, but while you are learning it pays mega dividends to be armed to the teeth with safety equipement. I have taught a lot of guys and a few gals how to cut their own wood for the winter and often have fielded complaints about the safety equipement I make em wear, but as of today I have never had a newbie go home injured.
Take your time,learn from someone who has more experience than you do any chance that you can, and have some fun with it.Just dont compromise safety for fun or a time schedule!