Investigating public attitudes on social media is crucial for opinion mining systems. Stance detection aims to predict the attitude towards a specific target expressed in a text. However, effective neural stance detectors require substantial training data, which are challenging to curate due to the dynamic nature of social media. Moreover, deep neural networks (DNNs) lack explainability, rendering them unsuitable for scenarios requiring explanations. We propose a distantly supervised explainable stance detection framework (DS-ESD), comprising an instruction-based chain-of-thought (CoT) method, a generative network, and a transformer-based stance predictor. The CoT method employs prompt templates to extract stance detection explanations from a very large language model (VLLM). The generative network learns the input-explanation mapping, and a transformer-based stance classifier is trained with VLLM-annotated stance labels, implementing distant supervision. We propose a label rectification strategy to mitigate the impact of erroneous labels. Experiments on three benchmark datasets showed that our model outperformed the compared methods, validating its efficacy in stance detection tasks. This research contributes to the advancement of explainable stance detection frameworks, leveraging distant supervision and label rectification strategies to enhance performance and interpretability.