Goal PET is a relatively noisy process compared to other imaging modalities, and sparsity of acquisition data leads to noise in the images. Recent work has focused on machine learning techniques to improve PET images, and this study investigates a deep learning approach to improve the quality of reconstructed image volumes through denoising by a 3D convolution neural network. Potential improvements were evaluated within a clinical context by physician performance in a reading task. Methods A wide range of controlled noise levels was emulated from a set of chest PET data in patients with lung cancer, and a convolutional neural network was trained to denoise the reconstructed images using the full-count reconstructions as the ground truth. The benefits, over conventional Gaussian smoothing, were quantified across all noise levels by observer performance in an image ranking and lesion detection task. Results The CNN-denoised images were generally ranked by the physicians equal to or better than the Gaussian-smoothed images for all count levels, with the largest effects observed in the lowest-count image sets. For the CNN-denoised images, overall lesion contrast recovery was 60% and 90% at the 1 and 20 million count levels, respectively. Notwithstanding the reduced lesion contrast recovery in noisy data, the CNN-denoised images also yielded better lesion detectability in low count levels. For example, at 1 million true counts, the average true positive detection rate was around 40% for the CNN-denoised images and 30% for the smoothed images. Conclusion Significant improvements were found for CNN-denoising for very noisy images, and to some degree for all noise levels. The technique presented here offered however limited benefit for detection performance for images at the count levels routinely encountered in the clinic.