Deep convolutional neural networks (CNN) have shown their good performances in many computer vision tasks. However, the high computational complexity of CNN involves a huge amount of data movements between the computational processor core and memory hierarchy which occupies the major of the power consumption. This paper presents Chain-NN, a novel energy-efficient 1D chain architecture for accelerating deep CNNs. Chain-NN consists of the dedicated dual-channel process engines (PE). In Chain-NN, convolutions are done by the 1D systolic primitives composed of a group of adjacent PEs. These systolic primitives, together with the proposed column-wise scan input pattern, can fully reuse input operand to reduce the memory bandwidth requirement for energy saving. Moreover, the 1D chain architecture allows the systolic primitives to be easily reconfigured according to specific CNN parameters with fewer design complexity. The synthesis and layout of Chain-NN is under TSMC 28nm process. It costs 3751k logic gates and 352KB on-chip memory. The results show a 576-PE Chain-NN can be scaled up to 700MHz. This achieves a peak throughput of 806.4GOPS with 567.5mW and is able to accelerate the five convolutional layers in AlexNet at a frame rate of 326.2fps. 1421.0GOPS/W power efficiency is at least 2.5 to 4.1x times better than the state-of-the-art works.