The custom of studying a daily portion of Chumash from the weekly Sedra dates back hundreds of years.

The Ba’al HaTanya & Shulchan Aruch, Rabbi Schneur Zalman of Liadi instituted the practice of studying the weekly Sedra – accompanied by Rashi’s commentary – one portion per day.
– Hayom Yom

“Rashi’s commentary on Chumash is the ‘wine’ of Torah. It unlocks one’s heart and reveals one’s innate and elemental love and awe [of G-d]”.
– Ba’al HaTanya V’Shulchan Aruch, The Alter Rebbe

The Alter Rebbe once announced “One ought to live with the times!” Chassidim were puzzled by the meaning of these words. Later, it was explained, that this means, not only to study the weekly Parsha, but to live with it, incorporating its lessons into our own life as a personal experience.
– Hayom Yom

“One ought to be scrupulous about the observance of studying a portion of Chumash with Rashi’s commentary each day (Sunday until Sheini, Monday until Shlishi, etc.). This affects him, his children and grandchildren.”
– The Previous Lubavitcher Rebbe, Rabbi Yosef Yitzchok

“Studying a parshah of Chumash every day with the commentary of Rashi activates the light in the soul and the revelation of the soul – which is a glow of the revelation of Mashiach.”
– Kovetz Lubavitch

“This custom is not only for Chassidim, but for all Jews.”
– The Previous Lubavitcher Rebbe, Rabbi Yosef Yitzchok

The Sha’ar HaMitzvos writes that the holy Arizal would study the portion of the week’s Sedra each day after Shachris, while wearing Talis & Tefillin.

The Lubavitcher Rebbe זי”ע – in his letters to Jews of all persuasions and often in response to requests for blessings regarding wellbeing – continuously urges the daily study of Chumash with Rashi (as part of ‘Chitas’: the daily study of Chumash, Tehillim & Tanya) and emphasizes the tremendous fringe benefit this brings in all areas of one’s life, serving as a broad conduit for Divine countenance.