A deep learning classifier for detecting seizures in neonates is proposed. This architecture is designed to detect seizure events from raw electroencephalogram (EEG) signals as opposed to the state-of-the-art hand engineered feature-based representation employed in traditional machine learning based solutions. The seizure detection system utilises only convolutional layers in order to process the multichannel time domain signal and is designed to exploit the large amount of weakly labelled data in the training stage. The system performance is assessed on a large database of continuous EEG recordings of 834h in duration; this is further validated on a held-out publicly available dataset and compared with two baseline SVM based systems. The developed system achieves a 56% relative improvement with respect to a feature-based state-of-the art baseline, reaching an AUC of 98.5%; this also compares favourably both in terms of performance and run-time. The effect of varying architectural parameters is thoroughly studied. The performance improvement is achieved through novel architecture design which allows more efficient usage of available training data and end-to-end optimisation from the front-end feature extraction to the back-end classification. The proposed architecture opens new avenues for the application of deep learning to neonatal EEG, where the performance becomes a function of the amount of training data with less dependency on the availability of precise clinical labels.