For heat conduction along polymer chains, a decrease in the axial thermal conductivity often occurs when the polymer structure changes from one-dimensional (1D) to three-dimensional (3D). For example, a single extended aliphatic chain (e.g., polyethylene or poly(dimethylsiloxane)) usually has a higher axial thermal conductivity than its double-chain or crystal counterparts because coupling between chains induces strong interchain anharmonic scatterings. Intuitively, for chains with an aromatic backbone, the even stronger π-π stacking, once formed between chains, should enhance thermal transport across chains and suppress the thermal conductivity along the chains. However, we show that this trend is the opposite in poly(p-phenylene) (PPP), a typical chain with an aromatic backbone. Using molecular dynamics simulations, we found that the axial thermal conductivity of PPP chains shows an anomalous dimensionality dependence where the thermal conductivity of double-chain and 3D crystal structures is higher than that of a 1D single chain. We analyzed the probability distribution of dihedral angles and found that π-π stacking between phenyl rings restricts the free rotation of phenyl rings and forms a long-range order along the chain, thus enhancing thermal transport along the chain direction. Though possessing a stronger bonding strength and stabilizing the multiple-chain structure, π-π stacking does not lead to a higher interchain thermal conductance between phenyl rings compared with that between aliphatic chains. Our simulation results on the effects of π-π stacking provide insights to engineer thermal transport in polymers at the molecular level.