Predicting all applicable labels for a given image is known as multi-label classification. Compared to the standard multi-class case (where each image has only one label), it is considerably more challenging to annotate training data for multi-label classification. When the number of potential labels is large, human annotators find it difficult to mention all applicable labels for each training image. Furthermore, in some settings detection is intrinsically difficult e.g. finding small object instances in high resolution images. As a result, multi-label training data is often plagued by false negatives. We consider the hardest version of this problem, where annotators provide only one relevant label for each image. As a result, training sets will have only one positive label per image and no confirmed negatives. We explore this special case of learning from missing labels across four different multi-label image classification datasets for both linear classifiers and end-to-end fine-tuned deep networks. We extend existing multi-label losses to this setting and propose novel variants that constrain the number of expected positive labels during training. Surprisingly, we show that in some cases it is possible to approach the performance of fully labeled classifiers despite training with significantly fewer confirmed labels.