Recurrent Neural Networks (RNNs) capture long dependencies and context, and 2 hence are the key component of typical sequential data based tasks. However, the sequential nature of RNNs dictates a large inference cost for long sequences even if the hardware supports parallelization. To induce long-term dependencies, and yet admit parallelization, we introduce novel shallow RNNs. In this architecture, the first layer splits the input sequence and runs several independent RNNs. The second layer consumes the output of the first layer using a second RNN thus capturing long dependencies. We provide theoretical justification for our architecture under weak assumptions that we verify on real-world benchmarks. Furthermore, we show that for time-series classification, our technique leads to substantially improved inference time over standard RNNs without compromising accuracy. For example, we can deploy audio-keyword classification on tiny Cortex M4 devices (100MHz processor, 256KB RAM, no DSP available) which was not possible using standard RNN models. Similarly, using SRNN in the popular Listen-Attend-Spell (LAS) architecture for phoneme classification [4], we can reduce the lag inphoneme classification by 10-12x while maintaining state-of-the-art accuracy.