Chronic stress can significantly affect physical and mental health. The advent of wearable technology allows for the tracking of physiological signals, potentially leading to innovative stress prediction and intervention methods. However, challenges such as label scarcity and data heterogeneity render stress prediction difficult in practice. To counter these issues, we have developed a multimodal personalized stress prediction system using wearable biosignal data. We employ self-supervised learning (SSL) to pre-train the models on each subject's data, allowing the models to learn the baseline dynamics of the participant's biosignals prior to fine-tuning the stress prediction task. We test our model on the Wearable Stress and Affect Detection (WESAD) dataset, demonstrating that our SSL models outperform non-SSL models while utilizing less than 5% of the annotations. These results suggest that our approach can personalize stress prediction to each user with minimal annotations. This paradigm has the potential to enable personalized prediction of a variety of recurring health events using complex multimodal data streams.