In this work, we studied the equilibrium structures formed by a single (AB)k multiblock copolymer chain. Within our model, the interactions between the A-type beads were repulsive and the B-type beads could form pairwise reversible bonds with each other (BB-bonds). Our goal was to investigate how the formation of pairwise reversible bonds between the A-type beads and the B-type beads (AB-bonds) affected the structure of the chain. We observed the formation of well-studied intramolecular micelles when the AB-bonds were absent; however, the chain folding changed dramatically when the formation of the AB-bonds was introduced. In this case, the multiblock copolymer formed a globule, which had a unique heterogeneous checkerboard-like distribution of the contact density. We discovered that contacts of beads of different types (i.e., AB-contacts) occurred much more frequently than contacts of beads of the same type (i.e., AA- and BB-contacts) in these structures. This effect can be explained by a simple model of chemical equilibrium in a two-component fluid of reversibly interacting particles, which can be solved exactly. This novel type of folding can serve as a basic model for any (AB)k multiblock copolymer chain with a non-vanishing attraction between A and B blocks.