We propose the task of Narrative Reordering(NAREOR) which involves rewriting a given story in a different narrative order while preserving its plot, semantic, and temporal aspects. We present a dataset, NAREORC, with over 1000 human rewritings of stories within ROCStories in non-linear orders, and conduct a detailed analysis of it. Further, we propose novel initial task-specific training methods and evaluation metrics. We perform experiments on NAREORC using GPT-2 and Transformer models and conduct an extensive human evaluation. We demonstrate that NAREOR is a challenging task with potential for further exploration.