(1) Background: CIC-DUX4 sarcoma is a rare mesenchymal small round cell tumor which belongs to rare cancers that occupy a significant percentage of cancer cases as a whole, despite each being rare. Importantly, each rare cancer type has different features, and thus there is a need to develop a model that mimics the features of each of these cancers. We evaluated the idea that the chicken chorioallantoic membrane assay (CAM), a convenient and versatile animal model, can be established for the CIC-DUX4 sarcoma. (2) Methods: Patient-derived cell lines of CIC-DUX4 were applied. These cells were transplanted onto the CAM membrane and tumor formation was examined by H&E staining, immunohistochemistry and Western blotting. The CAM tumor was transferred onto a fresh CAM and was also used to form organoids. Retention of the fusion gene was examined. (3) Results: H&E staining as well as molecular characterization demonstrated the formation of the CIC-DUX4 tumor on the CAM membrane. Expression of cyclin D2 and ETV4 was identified. The CAM tumor was transferred to a fresh CAM to form the second-generation CAM tumor. In addition, we were successful in forming tumor organoids using the CAM tumor. Retention of the fusion gene CIC-DUX4 in the CAM, second-generation CAM, and in the CAM-derived organoids was confirmed by RT-PCR. (4) Conclusions: The CAM assay provides a promising model for CIC-DUX4 sarcoma.