。
I'm suffering from chronic constipation.
Literal
Chronic's constipation [with-で] am-suffering.
慢性的な is a na-adjective formed from 慢性 ('chronic') + 的, a productive suffix turning nouns into na-adjectives of quality or manner — 医学的 (medical), 経済的 (economic), 効果的 (effective). で marks the cause of the suffering — 'suffering from X.' 苦しんでいる uses ~ている for the ongoing state of suffering.