Recent breakthroughs in Deep Neural Networks (DNNs) have fueled a growing demand for domain-specific hardware accelerators (i.e., DNN chips). However, designing DNN chips is non-trivial because: (1) mainstream DNNs have millions of parameters and billions of operations; (2) the design space is large due to numerous design choices of dataflows, processing elements, memory hierarchy, etc.; and (3) there is an algorithm/hardware co-design need for the same DNN functionality to have a different decomposition that would require different hardware IPs and thus correspond to dramatically different performance/energy/area tradeoffs. Therefore, DNN chips often take months to years to design and require a large team of cross-disciplinary experts. To enable fast and effective DNN chip design, we propose AutoDNNchip - a DNN chip generator that can automatically produce both FPGA- and ASIC-based DNN chip implementation (i.e., synthesizable RTL code with optimized algorithm-to-hardware mapping) from DNNs developed by machine learning frameworks (e.g., PyTorch) for a designated application and dataset without humans in the loop. Specifically, AutoDNNchip consists of 2 integrated enablers: (1) a Chip Predictor, which can accurately and efficiently predict a DNN accelerator's energy, throughput, latency, and area based on the DNN model parameters, hardware configurations, technology-based IPs, and platform constraints; and (2) a Chip Builder, which can automatically explore the design space of DNN chips (including IP selections, block configurations, resource balancing, etc.), optimize chip designs via the Chip Predictor, and then generate synthesizable RTL code with optimized dataflows to achieve the target design metrics. Experimental results show that our Chip Predictor's predicted performance differs from real-measured ones by <10% when validated using 15 DNN models and 4 platforms (edge-FPGA/TPU/GPU and ASIC). Furthermore, DNN accelerators generated by our AutoDNNchip can achieve better (up to 3.86X improvement) performance than that of expert-crafted state-of-the-art FPGA- and ASIC-based accelerators, showing the effectiveness of AutoDNNchip. Our open-source code can be found at https://github.com/RICE-EIC/AutoDNNchip.git.