Here is a little on the history of the Liturgy of the Hours:
The early writings of the Christian Church bear witness to a prayer tradition that is rich in eschatological symbols. Christians were to be always praying. They struggled was not against human agents but against spiritual, cosmic forces that never slept. They knew neither the hour nor the day on which the messiah would return. They owed the divine an unlimited measure of gratitude not only for creation but for the redemption of that creation.
Throughout the early centuries of Christianity, preachers admonished Christians to spend their entire lives in prayer. They encouraged them to pray in the morning and the evening, to rise during the night and keep vigil. Tertullian even encouraged them to use the regularly announced watches of the day (at the third, sixth and ninth hours) to remind themselves of their obligation to render thanks to God. 1 For early Christians the question was never whether or not they should pray always, only how to accomplish such an extreme demand. Origen (died c.254) encouraged them to interpret acts of righteousness and mercy as acts of prayer so that they might fulfill the command to pray always.
So while Christians were entreated to pray always in their hearts and in their actions, they also gathered regularly at the beginning and end of each day to pray together. The choice of these times may or may not have been influenced by Jewish traditions that placed particular emphasis on daily prayers at the beginning and end of each day.
After Constantine's conversion, these prayer times (morning, evening, and sometimes in the middle of the night) became common in all the cathedrals throughout the empire. In the West, these services came to be called matins, vespers, and vigils.
Selections from
http://www.yale.edu/adhoc/research_reso ... hours.html