Ok, so let's clear some things up.
There's what Chabad chassidim do - very often mistakenly, and all too often from mouth to ear, a broken telephone effect takes place where the original minhag or nohag avalanches into some absurd doing that the newcomers to Judaism through Chabad take upon as a holy war of sorts - and then there's what actually has its source in the ways of Chassidus that the Rebbes of the Chabad movement stated or acted upon unequivically, and which whenever they were approached about such minhagim etc. etc. they always made sure to provide a source.
(A famous example is regarding nicknames - it is common Chassidic practice to give each other simple nicknames, like "Ahrale" instead of "Aharon," Fitche instead of Yosef, and so on, and this is done more particularly by some of the bigger figures in Chassidus, since they did not like emphasizing their egos with high, exalted titles, settling instead for nicknames. The Lubavitcher Rebbe ztz"l was asked regarding this custom and what is the source is Torah- and indeed he provided a specific scenario in Gemara where it is proven that this custom has a source (I will provide that source upon request, I don't have it off the top of my head).
Now, as to the matter at hand. The other answer mentioned the statement by the Previous Rebbe, and it is a commonly known one amongst Chabad Chassidim. When such a tzaddik as the Rebbe says any given statement, it is not taken lightly. So Chassidim of the last Lubavitcher Rebbe tried to place a sefer atop of Tanya, and indeed when the Rebbe approached his shtender, he removed it from the Tanya. The next time, they tried to place a Tanya atop of a Chumash, and again with the Chumash atop the Tanya, and each time the Rebbe removed one from the other.
Chabad Chassidim thereby, based on the Rebbe's actions, took upon themselves the same hanhaga of not placing another sefer on top of Tanya, treating it as the Torah sh'bichtav of Chassidus. Most certainly, the Tanya should not be placed on top of a Chumash, that is against a very clear halacha in Sh"A.
I believe others mentioned the sources, but Halachically speaking, the only issur of placing one sefer atop of the other (and indeed the need to remove one from another) is only in regards to Tanach. Regarding other sefarim, it is silly if Chabad Chassidim have the hanhagga of placing Chassidic works davka atop of other works, and removing other works from atop of Chassidic works. Certainly one must comply with halacha, and then the only real established minhag by Chabad Chassidim is regards to Sefer haTanya, which is treated as one might Tanach, but certainly not at the expense of the latter.