In this paper, a novel framework is proposed for channel charting (CC)-aided localization in millimeter wave networks. In particular, a convolutional autoencoder model is proposed to estimate the three-dimensional location of wireless user equipment (UE), based on multipath channel state information (CSI), received by different base stations. In order to learn the radio-geometry map and capture the relative position of each UE, an autoencoder-based channel chart is constructed in an unsupervised manner, such that neighboring UEs in the physical space will remain close in the channel chart. Next, the channel charting model is extended to a semi-supervised framework, where the autoencoder is divided into two components: an encoder and a decoder, and each component is optimized individually, using the labeled CSI dataset with associated location information, to further improve positioning accuracy. Simulation results show that the proposed CC-aided semi-supervised localization yields a higher accuracy, compared with existing supervised positioning and conventional unsupervised CC approaches.