The Catholic Encyclopedia traces the story to the preaching of the Dominican Alan de la Roche around 1470 to 1475 and credits a Carthusian, Dominic of Prussia, with joining meditations on Christ's life to the Hail Marys. Counting prayers on beads is older than both. The same encyclopedia says the question involves no point of doctrine: it is a matter of history, and no Catholic is bound to hold that the vision took place.
St. John Paul II's 2002 letter on the Rosary does not name St. Dominic as its author; it says the prayer was used in particular by the Dominicans at a difficult time for the Church. Benedict XVI, speaking of St. Dominic in 2010, credited his spiritual sons with the great merit of spreading the prayer of the Holy Rosary.
Pilgrims meet the tradition in the places of his life. St. Dominic founded a convent at Prouilhe (Prouille), in the countryside of southern France where the story is set, in 1206; his Order of Preachers took shape in Toulouse; and he died in 1221 in Bologna, where he is buried. In Rome the Dominicans have been at Santa Sabina on the Aventine since his lifetime. At Pompei, near Naples, the shrine's venerated painting shows Our Lady of the Rosary with St. Dominic and St. Catherine of Siena. In each of these places the story is told as a tradition. None of this lessens the Rosary, whose value rests on the Gospel it contemplates, or the honor due to St. Dominic, whose friars carried it to the world.