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For a simple normal crossing variety $X$, we introduce the concepts of prelogChow ring, saturated prelog Chow group, as well as their counterparts fornumerical equivalence. Thinking of $X$ as the central fibre in a (strictly)semistable degeneration, these objects can intuitively be thought of asconsisting of cycle classes on $X$ for which some initial obstruction to ariseas specializations of cycle classes on the generic fibre is absent. Cycleclasses in the generic fibre specialize to their prelog counterparts in thecentral fibre, thus extending to Chow rings the method of studying smoothvarieties via strictly semistable degenerations. After proving basic propertiesfor prelog Chow rings and groups, we explain how they can be used in anenvisaged further development of the degeneration method by Voisin et al. toprove stable irrationality of very general fibres of certain families ofvarieties; this extension would allow for much more singular degenerations,such as toric degenerations as occur in the Gross-Siebert programme, to beusable. We illustrate that by looking at the example of degenerations ofelliptic curves, which, although simple, shows that our notion of prelogdecomposition of the diagonal can also be used as an obstruction in cases whereall components in a degeneration and their mutual intersections are rational.  We also compute the saturated prelog Chow group of degenerations of cubicsurfaces.

Prelog Chow rings and degenerations