Online and offline handwritten Chinese text recognition (HTCR) has been studied for decades. Early methods adopted over-segmentation-based strategies but suffered from low speed, insufficient accuracy, and high cost of character-level segmentation annotations. Recently, segmentation-free methods based on hidden Markov model (HMM), connectionist temporal classification (CTC), and attention mechanism, have dominated the field of HCTR. However, people actually read texts character by character, especially for ideograms like Chinese. This raises a question, are segmentation-free strategies really the best solution to HCTR To explore this issue, we propose a new segmentation-based method for recognizing handwritten Chinese text that is implemented using an efficient fully convolutional network. A novel weakly supervised learning method is proposed to enable the network to be trained using only transcript annotations; thus, the expensive character-level segmentation annotations required by previous segmentation-based methods can be avoided. Owing to the lack of context modeling in fully convolutional networks, we further propose a contextual regularization method to integrate contextual information into the network during the training stage, which can further improve the recognition performance. Extensive experiments on four widely used benchmarks, namely CASIA-HWDB, CASIA-OLHWDB, ICDAR2013, and SCUT-HCCDoc, show that our method significantly surpasses existing methods on both online and offline HCTR, and exhibits considerably higher inference speed than CTC/attention-based approaches.