Old (80s) dancehall language. Is a statement of respect or agreement which was assimilated by the 90s jungle scene. Similar to maximum respect. Back in the dancehall days, if the dance was told to big up dem chest or puff out them chest, they would physically push their chest out...
Person A: What did you think of my new track, man?
Person B: Tearin mate, big up your chest!
by p0lym0rph3 June 4, 2011
Get the big up your chest mug.