Polyethyleneimine (PEI), well known for its gene transfection studies. Generally, PEI is complexed with oppositely charged molecules to derive polyplexes to be used for various drug delivery applications. The release mechanism of these molecules from the polyplexes is highly dependent on the pH of the surroundings. pH can modulate the charge and the conformation of PEI chains leading to changes in its transfection efficiency. The effect of pH on the polyplexes has not been well understood, moreover, not even for pure PEI chains in aqueous solutions.  Our initial experimental observations suggest that at pH values between 2.5 to 4, neat PEI chains in explicit water undergo a completely unprecedented and never observed before kind of self-assembly process. The self-assembly is extremely slow, irreversible, and occurs under quiescent conditions to form a 3-D fibrillar network comprising hollow fibrils. The transition of PEI {≈ O (nm)} chains into micron-sized fibrillar network follows coalescence of smaller PEI chains to form ≈100-200 nm spheroidal aggregates accompanied with conformational/ morphological transitions into anisotropic rod-like aggregates which assemble end-to-end to form a network structure. We believe that our work will initiate to seek more understanding in the gene delivery through hyperbranched PEI-based polyplexes that occur under low pH conditions.