Hi.
Longman dictionary presents broil as an American variant of grill in British English.
http://www.ldoceonline.com/dictionary/broil Having lived in America, I personally hear people more say grilled chicken than broiled chicken. However, on my stove broil is written, but I think grill is more common even in American English.
I would be grateful if native speakers can stop by at this post and express their opinions about it.
Thank you for your time and help