have a pain in one's chest; feel tightness in the chest
Describes physical chest discomfort, pressure, or pain. Can also be used figuratively for emotional distress, but the physical sense is the focus here.
Lately, my chest feels tight when I climb stairs.
I had chest pain and went to the hospital.
Compound of 胸 (chest) + が (subject marker) + 苦しい (painful, tight). The expression is transparent and follows standard Japanese grammar.