There is an undeniable communication barrier between deaf people and people with normal hearing ability. Although innovations in sign language translation technology aim to tear down this communication barrier, the majority of existing sign language translation systems are either intrusive or constrained by resolution or ambient lighting conditions. Moreover, these existing systems can only perform single-sign ASL translation rather than sentence-level translation, making them much less useful in daily-life communication scenarios. In this work, we fill this critical gap by presenting DeepASL, a transformative deep learning-based sign language translation technology that enables ubiquitous and non-intrusive American Sign Language (ASL) translation at both word and sentence levels. DeepASL uses infrared light as its sensing mechanism to non-intrusively capture the ASL signs. It incorporates a novel hierarchical bidirectional deep recurrent neural network (HB-RNN) and a probabilistic framework based on Connectionist Temporal Classification (CTC) for word-level and sentence-level ASL translation respectively. To evaluate its performance, we have collected 7, 306 samples from 11 participants, covering 56 commonly used ASL words and 100 ASL sentences. DeepASL achieves an average 94.5% word-level translation accuracy and an average 8.2% word error rate on translating unseen ASL sentences. Given its promising performance, we believe DeepASL represents a significant step towards breaking the communication barrier between deaf people and hearing majority, and thus has the significant potential to fundamentally change deaf people's lives.