This practice has been variously called 'the Jesus Prayer,' the 'Prayer of the Heart,' and the 'Way of the Name.' It has been handed down from the earliest centuries of the Church through the Orthodox tradition, where it is still practiced. Extensive discussion of the method is recorded in the Orthodox compendium called the 'Philocalia,' which contains writings from the 5th through 19th Centuries. This living tradition of Christian meditation continues not only in Eastern Orthodox Churches, but among American Protestants, Catholics, Quakers and other seekers as well. A more systematic essay on Prayer of the Heart is found at the following link on this site: LINK.
India has a venerable tradition of Mantra Yoga, meditation through the divine Name. In Islam, the 99 Names of Allah are seeds of devotion and prayer. In Jewish mysticism, the ascent of the soul to God is through the divine name as well. Just so, in Orthodox Christianity, the core experience of prayer is inner silence -'hesychasm' - gracefully attained through the Name of the Lord, which carries us into the heart by means of breathing.
1. Old Testament: "The Still Small Voice"
This well-known phrase from the Elijah saga in 1 Kings literally means “a voice of murmuring finely ground silence,” in Hebrew: qol d’mama d’aqah. Christian mystics have loved this passage describing the "still small voice of calm" within. Throughout the earliest Old Testament texts, "calling on the Name of the Lord" is recorded as the most ancient spiritual practice in the Bible. Indeed, all of creation happens through the Word. The Psalms declare, "Through the Word of the Lord were the heavens made, and all their hosts by the breath of his mouth." The practice of prayer through the Name of God is simply creation in reverse: We enter the divine all-creative silence by following the vibration of the Word back to its source.
2. New Testament
'Hallowed be thy Name..." (Mat 6)
"Keep them in your Name that they may be one, as we are one... I have revealed your Name to them... so that the love with which you loved me may be in them, and I may be in them." (John 17)
"No one enters the Kingdom of God except through the Name of his Son... The Name of the Son of God is great and boundless, and it is this Name that upholds the entire world." (Shepherd of Hermes, 3.9.12-14)
"He who possesses the Word of Jesus can hear his very silence and become perfect." (St. Ignatius to the Ephesians 3:21)
"Jesus is a secret Name... For that reason Jesus does not exist in any other language... There is only one Name which one does not speak out in the world, the Name which the Father gave to the Son. It is above everything." (Gnostic Gospel of Philip)
"The Name which is above every Name..." (Philippians 2:9)
"They are called Sons of the Name... in whom the Name of the Father is at rest, and they are at rest in his Name." (Gnostic Gospel of Truth)
3. Eastern Orthodoxy: 'Prayer of the Name' in The Philocalia
5th C. - "Sinai Tradition"
* 430 AD - St. Niles of Ancyra speaks of the "Invocation of the Name of Jesus."
6th C. - "Life of Abba Philemon"
• While recognizing shorter variants, such as the simple name of 'Jesus' itself, this work gives for the first time the complete formula of the 'Jesus Prayer': Lord Jesus Christ, Son of God, have mercy on me.
7th C. - St John Climacus ('The Divine Ladder')
• "Prayer is constant remembrance of our Lord Jesus Christ, quietly led into the heart by way of breathing and again led out, without any extraneous thought or imagining." (45)
• Monologistos eucharistos, "one-word prayer"; Iesou euche: "Jesus Prayer" (first use of the term)
8th C. - St. Hesychius of Jerusalem, "On Watchfulness and Holiness"
• "Constantly breathing Jesus Christ..."
• ...The heart's silence, unbroken by any thought: in this silence the heart breathes and invokes without ceasing only Jesus Christ, Son of God." (5)
• "The light of God begins to illumine the mind when it is freed of everything and totally empty of form. For this illumination is manifested in a mind that is pure, on condition that it is freed of all thoughts." (89)
13th C. - Nichodemus of the Holy Mountain (Mt. Athos)
• "Let Jesus be your breath."
14th C. - Philotheus, Mt. Athos, "Texts on Watchfulness"
• "Invoked in prayer, Jesus draws near and fills the heart with light." (29)
• "We must ceaselessly breathe God." (30)
14th C. - The Monks Callistus and Ignatius, Mt. Athos "Directions to Hesychasts"
• "After sunset, having asked the help of the all-merciful and all-powerful Lord Jesus Christ, sit you down on a low stool in your quiet and dimly lit cell; collect your mind from its customary circling and wandering outside, and quietly lead it into the heart by way of breathing, keeping the prayer, 'Lord Jesus Christ, Son of God, have mercy on me,' connected with the breath." (25)
• "As regards the words, 'have mercy on me', added to the salvation-working words of the prayer, 'Lord Jesus Christ, Son of God', it was added by the holy fathers chiefly for those who are still infants in the work of virtue, the beginners... For the advanced and the holy in Christ are content with any of the shorter forms, 'Lord Jesus', 'Jesus Christ', 'Christ Son of God', or even with one word, 'Jesus', which they kiss and embrace as the complete doing of prayer, sufficient to fill them with ineffable bliss and joy exceeding all mind, all vision and all hearing." (50)
19th C: "The Way of a Pilgrim" (anonymous Russian classic)
• "Sink down in silence into the depths of your heart and call more and more upon the radiant Name of Jesus. Everyone who does this will experience, at last, the Inward Light."
20th C: "Breath of the Mystic," (Fa. George Maloney, S.J.)
• "Ephesians 1:23 describes, 'The fullness of Him who fills all in all." By pronouncing the Holy Name of Jesus, we release this transfiguring power. We call Him into being to touch our suffering world groaning in travail. We ask Him to transform the universe."
• "God was meant to be man's breath. Man was meant to be healthy and full of life by breathing in the loving power of God."
LINK: 'Prayer of the Heart' (Essay, with guided meditation instructions)