A staunch companion to seismic signals, noise consistently hinders processing and interpretation of seismic data. Borrowing ideas from the field of computer vision, we propose the use of self-supervised deep learning for the task of random noise suppression. These techniques require no clean training data and therefore remove any requirement of pre-cleaning of field data or the generation of realistic synthetic datasets for training purposes. Through the use of blind-spot networks, we show that self-supervised Noise2Void (N2V) procedure can be adapted to the seismic context, and trained solely on noisy data. An initial validation performed on a synthetic dataset corrupted by additive, white, Gaussian noise confirms that N2V can be trained to accurately separate the correlated seismic signal from the uncorrelated noise. Furthermore, when correlated and random noise are both present in the data, whilst the model cannot remove the majority of the correlated noise, a portion of it is suppressed alongside the random noise. Finally, the network is validated on a field dataset that is heavily contaminated with strong random noise caused by the surface conditions. The N2V denoising approach is shown to drastically reduce the random noise in the data. Through these examples, we have validated the effectiveness of blind-spot networks on highly oscillating signals, such as seismic data. This pave the way for the application of other self-supervised procedures to seismic data that go beyond the assumption of statistically independent noise.