Motivic cohomology computes Chow groups. And, motivic cohomology is representable in the A^1-category. More specifically, CH^p(X)=H^2p(X,Z(p)). The cohomology groups on the right are representable by "Eilenberg-Mac Lane" spaces in A^1-homotopy theory. Here, by representable, I mean the cohomology groups coincide with homotopy classes of maps to some space.
Some more details: Marc Levine has a paper called The homotopy coniveau filtration; you can find it here. The title refers to a tower that is an analogue of the Gersten resolution in algebraic K-theory. The layers of the homotopy coniveau filtration for the space representing K-theory apparently give the motivic Eilenberg-Mac Lane spectrum.
Let me tell you the details. This is all from the introduction of Levine's paper. Let E be a spectrum (in the stable motivic category). For such a spectrum E, Levine constructs a tower E^(p)->E^(p-1)->...->E. E^(p)(X) is the limit of the spectra with supports E^W(XxA^n) where W is closed of codimension at least p in XxA^n. Then, the layer E^(p/p+1) is the cofiber at level p. When applied to the spectrum representing K-theory, the slice K^(p/p+1)(X) corresponds to Bloch's higher cycle group z^p(X). And, it is well known that this computes (higher) Chow groups and motivic cohomology.