challenge

First recorded in 1175–1225; Middle English chalenge, from Old French, variant of chalonge, from Latin calumnia “false statement”; see calumny

The English verb challenge comes from Middle English kalange(n), chalenge(n) “to accuse, claim,” which comes from the Old French verb calonger, calanger, chalonger, chalanger (with still more variants) “to protest, complain,” from Latin calumniārī “to bring false accusations, interpret wrongly, misrepresent, criticize unfairly,” itself a derivation of the noun calumnia, with legal meanings “false accusation, false claim, false pretenses, the making of unfounded objections, trickery.” (The Old French noun chalenge, chalonge is a regular development of Latin calumnia: the cluster -mni- becomes -nge in French, as Latin somnium “dream” becomes Old French songe with the same meaning.)
Latin calumnia is the direct source of calumny, “a false and malicious statement,” so calumny and challenge are doublets (words deriving ultimately from the same source). In fact, an earlier, now obsolete meaning of challenge was “an accusation or false claim.”
The legal sense of challenge, “to object to (a juror or evidence),” dates from the 16th century. The verb sense “to summon someone to a fight or a duel” first appears in Shakespeare’s Love’s Labour’s Lost (1598).