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We define the Chow t-structure on the ∞-category of motivic spectra SH(k) over an arbitrary base field k. We identify the heart of this t-structure SH(k)c♡ when the exponential characteristic of k is inverted. Restricting to the cellular subcategory, we identify the Chow heart SH(k)cell,c♡ as the category of even graded MU2∗MU-comodules. Furthermore, we show that the ∞-category of modules over the Chow truncated sphere spectrum 1c=0 is algebraic. Our results generalize the ones in Gheorghe–Wang–Xu in three aspects: to integral results; to all base fields other than just C; to the entire ∞-category of motivic spectra SH(k), rather than a subcategory containing only certain cellular objects. We also discuss a strategy for computing motivic stable homotopy groups of (p-completed) spheres over an arbitrary base field k using the Postnikov–Whitehead tower associated to the Chow t-structure and the motivic Adams spectral sequences over k.