[The Chicago-Lambeth Quadrilateral is the ]statement of the four Anglican essentials for a reunited Christian Church. It concerns the scriptures, creeds, sacraments, and the historic episcopate. It was approved by the House of Bishops at the 1886 General Convention in Chicago, and subsequently approved with modifications by the bishops of the Anglican Communion at the Lambeth Conference of 1888.
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The four points of the Quadrilateral were listed by the Chicago statement as "inherent parts" of the sacred deposit of Christian faith and order "committed by Christ and his Apostles to the Church unto the end of the world, and therefore incapable of compromise or surrender. . . ." The Chicago statement lists the Nicene Creed as the sufficient statement of the Christian faith. With respect to baptism and the eucharist, the Chicago statement calls for administration of these sacraments "with unfailing use of Christ's words of institution and of the elements ordained by Him." The Chicago version expressed the fourth part of the Quadrilateral in terms of "The Historic Episcopate, locally adapted in the methods of its administration to the varying needs of the nations and peoples called of God into the unity of His Church." Although the Quadrilateral was not enacted by the House of Deputies at the 1886 General Convention, it was incorporated in a general plan referred for study and action by the newly created Joint Commission on Christian Reunion.
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At the 1895 General Convention of the Episcopal Church, the Commission on Christian Unity was continued with the goal of seeking Christian unity on the basis of the "principles enunciated throughout the Declaration of the house of Bishops made at Chicago in 1886, and as reaffirmed by the Lambeth Conference of 1888." Thus for the first time the entire General Convention of the Episcopal Church affirmed the Quadrilateral in its Lambeth form. The Chicago-Lambeth Quadrilateral has continued to serve as the primary Anglican working document and reference point for ecumenical Christian reunion. The Chicago and Lambeth versions of the Quadrilateral are included in the historical documents of the 1979 BCP (pp. 876-878).

Source: Episcopalchurch.org - "Chicago-Lambeth Quadrilateral", glossary entry for episcopalchurch.org
https://www.episcopalchurch.org/library/glossary/chicago-lambeth-quadrilateral

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