Medical imaging devices, such as X-ray machines, inherently produce images that suffer from visual noise. Our objectives were to (i.) determine the effect of image denoising on a medical image classification task, and (ii.) determine if there exists a correlation between image denoising performance and medical image classification performance. We performed the medical image classification task on chest X-rays using the DenseNet-121 convolutional neural network (CNN) and used the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) metrics as the image denoising performance measures. We first found that different denoising methods can make a statistically significant difference in classification performance for select labels. We also found that denoising methods affect fine-tuned models more than randomly-initialized models and that fine-tuned models have significantly higher and more uniform performance than randomly-initialized models. Lastly, we found that there is no significant correlation between PSNR and SSIM values and classification performance for our task.