Chainsaws and brush don't always mix well. The chain tends to grab and fling small stuff instead of cutting through it. It is also liable to throw the chain off the bar. Almost invariably, that causes a burr on some of the guide teeth which you'll have to file down before the chain will fit back in the groove.

I'm not an expert chainsaw operator by any standard, but so far, I have been able to keep arms, legs and head attached. That out of the way, the most dangerous part of the saw is the tip's upper quadrant. If it bites in, it will kick the saw up and towards you - always be mindful of where the tip is (and of what is near it.)

Use all the safety gear you can get you're hands on - chainsaw chaps, goggles/face shield, hard hat. steel toe boots. (The brambles may be hiding something hard.)

Chainsaws are right handed tools. If you're left handed, be extra careful of what you're doing.

When cutting from the top (with the bottom chain), the motion pulls the saw into the log - pretty safe. When cutting from underneath, the chain will push the saw towards you (and that upper quadrant towards the danger area...)

Lock your left elbow when cutting. If it does kick, the saw will rotate around your wrist and engage the chain brake (on a gas powered saw, that is.)

Keep your body out of the plane of the cut. Better chance it'll miss your head if it kicks back.

Most saws these days leave the shop with a safety chain. These have links with depth gauges between the cutting links to limit the bite when the chain rounds the tip. If yours left the internet with a non-safety chain, consider replacing it.

Keep the cutters sharp. It's safer to operate if it works properly.

http://www.tcia.org/TCIA/Publications/TCI_Magazine/HTMLpages/October2016/Chain_Saw_Safety__Understanding_Rotational_Kickback.aspx