In contrast to non-medical image denoising, where enhancing image clarity is the primary goal, medical image denoising warrants preservation of crucial features without introduction of new artifacts. However, many denoising methods that improve the clarity of the image, inadvertently alter critical information of the denoised images, potentially compromising classification performance and diagnostic quality. Additionally, supervised denoising methods are not very practical in medical image domain, since a \emph{ground truth} denoised version of a noisy medical image is often extremely challenging to obtain. In this paper, we tackle both of these problems by introducing a novel neural network based method -- \emph{Contextual Checkerboard Denoising}, that can learn denoising from only a dataset of noisy images, while preserving crucial anatomical details necessary for image classification/analysis. We perform our experimentation on real Optical Coherence Tomography (OCT) images, and empirically demonstrate that our proposed method significantly improves image quality, providing clearer and more detailed OCT images, while enhancing diagnostic accuracy.