From the second day of Rosh Chodesh Elul it is customary to recite three chapters of Tehillim a day. We start from the first chapter, each day moving forward another three chapters. The final chapters are recited on Yom Kippur. One is not to recite more than the allotted three chapters a day as part of this order. If one missed the three chapters of a given day, then he should first recite the current day’s three chapters and make up the chapters he missed on a later occasion.
This custom was told to Tzemach Tzedek by his grandfather the Alter Rebbe when he was nine years old. The Alter Rebbe told him “I received from my master the Maggid, who received from his master the Baal Shem Tov, who received from his known teacher [Achiya Hashiloni].” Thus the custom dates back to Achiya Hashiloni which was one of the Sages listed as part of the continuity of the Torah Shebaal Peh. [Rambam Hakdama]