Using a Monte Carlo simulation technique, we have modeled the process of copolymerization of hydrophobic and hydrophilic monomers in a selective (polar) solvent. The composition of an emerging polymer chain is such that macromolecule adopts a globular conformation. The preferential sorption of hydrophobic monomers in the core of the globule is explicitly taken into account. It is shown that such the copolymerization process automatically leads to the formation of the core-shell microstructure in the resulting globule and to the well-pronounced long-range correlations of the Levy-flight type in obtained sequences of monomer units. Thus, this type of synthesis provides a robust one-step method of producing of "proteinlike" copolymers, i.e., copolymers that exhibit in the globular state a microstructure with a hydrophobic core wrapped in a hydrophilic envelope. (C) 2003 American Institute of Physics.