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Recently, there has been a surge of significant interest on application of Deep Learning (DL) models to autonomously perform hand gesture recognition using surface Electromyogram (sEMG) signals. DL models are, however, mainly designed to be applied on sparse sEMG signals. Furthermore, due to their complex structure, typically, we are faced with memory constraints; require large training times and a large number of training samples, and; there is the need to resort to data augmentation and/or transfer learning. In this paper, for the first time (to the best of our knowledge), we investigate and design a Vision Transformer (ViT) based architecture to perform hand gesture recognition from High Density (HD-sEMG) signals. Intuitively speaking, we capitalize on the recent breakthrough role of the transformer architecture in tackling different complex problems together with its potential for employing more input parallelization via its attention mechanism. The proposed Vision Transformer-based Hand Gesture Recognition (ViT-HGR) framework can overcome the aforementioned training time problems and can accurately classify a large number of hand gestures from scratch without any need for data augmentation and/or transfer learning. The efficiency of the proposed ViT-HGR framework is evaluated using a recently-released HD-sEMG dataset consisting of 65 isometric hand gestures. Our experiments with 64-sample (31.25 ms) window size yield average test accuracy of 84.62 +/- 3.07%, where only 78, 210 number of parameters is utilized. The compact structure of the proposed ViT-based ViT-HGR framework (i.e., having significantly reduced number of trainable parameters) shows great potentials for its practical application for prosthetic control.