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The Benediction of the Blessed Sacrament is the result of a confluence of two separate traditions dating back to the thirteenth century. Exposing the Blessed Sacrament for veneration in a monstrance grew out of special value being placed upon the act of looking at the elevation of the Eucharist at mass, probably as a form of protest against the theological views of Peter the Chanter. The second tradition, an evening devotion consisting of the singing of certain hymns, litanies, or canticles before the Blessed Sacrament developed from the many confraternities and guilds that sang canticles in the evening before a statue of "Our Lady".
Summarized from the Benediction of the Blessed Sacrament entry in the 1917 Catholic Encyclopedia