Precise localization is critical for autonomous vehicles. We present a self-supervised learning method that employs Transformers for the first time for the task of outdoor localization using LiDAR data. We propose a pre-text task that reorganizes the slices of a $360^\circ$ LiDAR scan to leverage its axial properties. Our model, called Slice Transformer, employs multi-head attention while systematically processing the slices. To the best of our knowledge, this is the first instance of leveraging multi-head attention for outdoor point clouds. We additionally introduce the Perth-WA dataset, which provides a large-scale LiDAR map of Perth city in Western Australia, covering $\sim$4km$^2$ area. Localization annotations are provided for Perth-WA. The proposed localization method is thoroughly evaluated on Perth-WA and Appollo-SouthBay datasets. We also establish the efficacy of our self-supervised learning approach for the common downstream task of object classification using ModelNet40 and ScanNN datasets. The code and Perth-WA data will be publicly released.