Wiktionary says that Elita was first recorded as a given name of Latvians during 1850 - 1875. Possibly from French élite ("elite"), or a phonetic coinage.
― Anonymous User 9/30/2012
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Means "The Chosen One". Of Latin and French origin from the Latin word "elite" which was taken from the French word "élire" meaning "to choose". Also short form of names ending in "elita" or "lita".