hemicrania
n. hem·i·cra·nia
From Late Latin hemicrania (“pain in one half of the head”), from Ancient Greek ἡμικρᾱνίᾰ (hēmikrāníă), from ἡμι- (hēmi-, “hemi-, half”) + κρανίον (kraníon, “skull”) (from whence also cranium). Cognate to megrim and migraine, which also derive from the Latin.