Where did the Rosary come from? Is the Catholic Church the only Christian Church that prays this devotion?
It is commonly held that St Dominic was the person who first started the practice of the recitation of the Rosary. There is, however, limited evidence of this and different versions of how it originated. This article gives some background on the role of St Dominic.
There were other persons involved in developing the structure of the Rosary that we have today, as you can read here. As with many of these traditions that go back so many centuries we have limited historical knowledge of how they originated.
Some of the Eastern and Orthodox churches do have devotion to Mary and even in some Anglican churches they have statues to Mary. You can read about some of these practices here.
A number of the Protestant churches, however, rejected many of the devotional customs of the Catholic Church, choosing to simply base themeselves on Scripture and on Christ, and rejecting any devotion to Mary, the Saints and many other practices that we still have today in the Catholic Church.