Chromosome recognition is an essential task in karyotyping, which plays a vital role in birth defect diagnosis and biomedical research. However, existing classification methods face significant challenges due to the inter-class similarity and intra-class variation of chromosomes. To address this issue, we propose a supervised contrastive learning strategy that is tailored to train model-agnostic deep networks for reliable chromosome classification. This method enables extracting fine-grained chromosomal embeddings in latent space. These embeddings effectively expand inter-class boundaries and reduce intra-class variations, enhancing their distinctiveness in predicting chromosome types. On top of two large-scale chromosome datasets, we comprehensively validate the power of our contrastive learning strategy in boosting cutting-edge deep networks such as Transformers and ResNets. Extensive results demonstrate that it can significantly improve models' generalization performance, with an accuracy improvement up to +4.5%. Codes and pretrained models will be released upon acceptance of this work.