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Recently, Transformer has gained success in automatic speech recognition (ASR) field. However, it is challenging to deploy a Transformer-based end-to-end (E2E) model for online speech recognition. In this paper, we propose the Transformer-based online CTC/attention E2E ASR architecture, which contains the chunk self-attention encoder (chunk-SAE) and the monotonic truncated attention (MTA) based self-attention decoder (SAD). Firstly, the chunk-SAE splits the speech into isolated chunks. To reduce the computational cost and improve the performance, we propose the state reuse chunk-SAE. Sencondly, the MTA based SAD truncates the speech features monotonically and performs attention on the truncated features. To support the online recognition, we integrate the state reuse chunk-SAE and the MTA based SAD into online CTC/attention architecture. We evaluate the proposed online models on the HKUST Mandarin ASR benchmark and achieve a 23.66% character error rate (CER) with a 320 ms latency. Our online model yields as little as 0.19% absolute CER degradation compared with the offline baseline, and achieves significant improvement over our prior work on Long Short-Term Memory (LSTM) based online E2E models.