Distributed massive MIMO is considered a key advancement for improving the performance of next-generation wireless telecommunication systems. However, its efficacy in scenarios involving user mobility is limited due to channel aging. To address this challenge, channel prediction techniques are investigated to forecast future channel state information (CSI) based on previous estimates. We propose a new channel prediction method based on channel charting, a self-supervised learning technique that reconstructs a physically meaningful latent representation of the radio environment using similarity relationships between CSI samples. The concept of inertia within a channel chart allows for predictive radio resource management tasks through the latent space. We demonstrate that channel charting can be used to predict future CSI by exploiting spatial relationships between known estimates that are embedded in the channel chart. Our method is validated on a real-world distributed massive MIMO dataset, and compared to a Wiener predictor and the outdated CSI in terms of achievable sum rate.