Images shared on social media are routinely analysed by classifiers for content annotation and user profiling. These automatic infer- ences reveal to the service provider sensitive information that a naive user might want to keep private. To address this problem, we present a method designed to distort the image data so as to hinder the inference of a classifier without affecting the utility for social media users. The proposed approach is based on the Fast Gradient Sign Method (FGSM) and limits the likelihood that automatic inference can expose the true class of a distorted image. Experimental results on a scene classification task show that the proposed method, private FGSM, achieves a desirable trade-off between the drop in classification accuracy and the distortion on the private classes of the Places365-Standard dataset using ResNet50. The classifier is misled 94.40% of the times in the top-5 classes with only a small average reduction of three image quality measures (SSIM, PSNR, BRISQUE).