Predicting the properties of molecules is a fundamental problem in drug design and discovery, while how to learn effective feature representations lies at the core of modern deep learning based prediction methods. Recent progress shows expressive power of graph neural networks (GNNs) in capturing structural information for molecular graphs. However, we find that most molecular graphs exhibit low clustering along with dominating chains. Such topological characteristics can induce feature squashing during message passing and thus impair the expressivity of conventional GNNs. Aiming at improving node features' expressiveness, we develop a novel chain-aware graph neural network model, wherein the chain structures are captured by learning the representation of the center node along the shortest paths starting from it, and the redundancy between layers are mitigated via initial residual difference connection (IRDC). Then the molecular graph is represented by attentive pooling of all node representations. Compared to standard graph convolution, our chain-aware learning scheme offers a more straightforward feature interaction between distant nodes, thus it is able to capture the information about long-range dependency. We provide extensive empirical analysis on real-world datasets to show the outperformance of the proposed method. The MolPath code is publicly available at https://github.com/Assassinswhh/Molpath. Supplementary information are available at Bioinformatics online.