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c.1200, from Old English conjunction oþþe "either, or," related to Old Frisian ieftha, Middle Dutch ofte, Old Norse eða, Old High German odar, German oder, Gothic aiþþau "or." This was extended in early Middle English (and Old High German) with an -r ending, perhaps by analogy with "choice between alternative" words that ended thus (e.g. either, whether), then reduced to oþþr, at first in unstressed situations (commonly thus in Northern and Midlands English by 1300), and finally reduced to or, though other survived in this sense until 16c.
The contraction took place in the second term of an alternative, such as either ... or, a common construction in Old English, where both words originally were oþþe (see nor).