R' Zev Dov Slonim compiled a booklet that collates various sources that talk about the advantage of learning Chumash, saying Tehillim, and Learning Tanya daily. The booklet is also included in the Chitas sefer, published by Kehot. The footnotes on Sefer Haminhagim's entry on Chitas discusses this as well.
Here are some of them, see sources inside for more:
- The Shibolei HaLeket (Inyan Tefilla #44), brings from Rashi that the early Chassidim would learn for an hour after prayer. He connects this to the idea brought in the Talmud (Kiddushin 30A) , that one should always split his his learning into three. A third Mikrah, a third Mishna, and a third Talmud.Rabbi Slonim points out that in Shulchan Aruch HaRav (Hilchot Talmud Torah, Chapter 2, Halacha 1), the Baal HaTanya says that explanations of the Written Torah fall under the heading of "Mishna" and Kabbalah falls under the catagory of "Talmud".Hence, learning Chitas daily covers Mikrah (Tehillim, Chumash), Mishna (Rashi on Chumash), and Talmud (Tanya).