WordNet sense 1 (marked by a large or well-developed chest):

big-chested

WordNet sense 2 (physically strong):

robust

WordNet sense 3 (having or showing feelings of unwarranted importance out of overbearing pride):

arrogant, self-important

WordNet sense 4 (feeling self-respect or pleasure in something by which you measure your self-worth; or being a reason for pride):

proud