The Council of Chalcedon was a church council held in 451 AD, at Chalcedon (a city of Bithynia in Asia Minor), on the Asian side of the Bosporus. This was a highly influential council and marked a key turning point in the Christological debates that broke apart the church of the Eastern Roman Empire in the 5th century. The Council of Chalcedon repudiated the idea that Jesus had only one nature, and stated that Christ has two natures in one person. The Chalcedonian Creed describes the “full humanity and full divinity” of Jesus, the second person of the Holy Trinity.
The Council is considered by the Roman Catholics, the Eastern Orthodox, the Old Catholics, and various other Western Christian groups to have been the Fourth Ecumenical Council. As such, it is recognized as infallible in its dogmatic definitions by the Roman Catholic and Eastern Orthodox Churches (then one church). Most Protestants also consider the concept of the Trinity as defined by these councils to be orthodox doctrine to which they adhere. (Background introduction adapted from Wiki)
Therefore, following the holy fathers, we all with one accord teach men to acknowledge one and the same Son, our Lord Jesus Christ, at once complete in Godhead and complete in manhood, truly God and truly man, consisting also of a reasonable soul and body; of one substance with the Father as regards his Godhead, and at the same time of one substance with us as regards his manhood; like us in all respects, apart from sin; as regards his Godhead, begotten of the Father before the ages, but yet as regards his manhood begotten, for us men and for our salvation, of Mary the Virgin, the God-bearer; one and the same Christ, Son, Lord, Only-begotten, recognized in two natures, without confusion, without change, without division, without separation; the distinction of natures being in no way annulled by the union, but rather the characteristics of each nature being preserved and coming together to form one person and subsistence, not as parted or separated into two persons, but one and the same Son and Only-begotten God the Word, Lord Jesus Christ; even as the prophets from earliest times spoke of him, and our Lord Jesus Christ himself taught us, and the creed of the fathers has handed down to us.