Coherent noise regularly plagues seismic recordings, causing artefacts and uncertainties in products derived from down-the-line processing and imaging tasks. The outstanding capabilities of deep learning in denoising of natural and medical images have recently spur a number of applications of neural networks in the context of seismic data denoising. A limitation of the majority of such methods is that the deep learning procedure is supervised and requires clean (noise-free) data as a target for training the network. Blindspot networks were recently proposed to overcome this requirement, allowing training to be performed directly on the noisy field data as a powerful suppressor of random noise. A careful adaptation of the blind-spot methodology allows for an extension to coherent noise suppression. In this work, we expand the methodology of blind-spot networks to create a blind-trace network that successfully removes trace-wise coherent noise. Through an extensive synthetic analysis, we illustrate the denoising procedure's robustness to varying noise levels, as well as varying numbers of noisy traces within shot gathers. It is shown that the network can accurately learn to suppress the noise when up to 60% of the original traces are noisy. Furthermore, the proposed procedure is implemented on the Stratton 3D field dataset and is shown to restore the previously corrupted direct arrivals. Our adaptation of the blind-spot network for self-supervised, trace-wise noise suppression could lead to other use-cases such as the suppression of coherent noise arising from wellsite activity, passing vessels or nearby industrial activity.Preprint. Under review.