Synthetic Aperture Radar (SAR) images are usually degraded by a multiplicative noise known as speckle which makes processing and interpretation of SAR images difficult. In this paper, we introduce a transformer-based network for SAR image despeckling. The proposed despeckling network comprises of a transformer-based encoder which allows the network to learn global dependencies between different image regions - aiding in better despeckling. The network is trained end-to-end with synthetically generated speckled images using a composite loss function. Experiments show that the proposed method achieves significant improvements over traditional and convolutional neural network-based despeckling methods on both synthetic and real SAR images.