late 14c., "practice oratory, make a formal speech or oration," from Old French declamer (Modern French déclamer) and directly from Latin declamare "to practice public speaking, to bluster," from de-, here probably an intensive prefix (see de-) + clamare "to cry, shout" (from PIE root *kele- (2) "to shout").
At first in English spelled declame, but altered under influence of claim. From 1570s as "speak or write as an exercise in elocution;" from 1795 as "speak aloud passionately in an appeal to the emotions of the audience." Related: Declaimed; declaiming.