Policy makers are actively investing in care programs that integrate Medicare and Medicaid benefits, with the goal of providing better-coordinated care for Medicare-Medicaid dual-eligible beneficiaries. However, nonintegrated plans have become increasingly popular among dual eligibles. One such plan type is the Chronic Condition Special Needs Plan (C-SNP)-a type of Medicare Advantage plan designed for people with specific chronic conditions. Using national Medicare data from the period 2011-24, we found that C-SNPs experienced modest enrollment growth among dual eligibles, with nearly 15 percent of C-SNP enrollees being full-benefit dual eligibles, who are eligible for Medicare and full Medicaid benefits. In 2024, among newly enrolled C-SNP full-benefit dual eligibles, 5.3 percent, 4.8 percent, and 14.9 percent were previously enrolled in plans with high, moderate, and low levels of Medicare-Medicaid integration, respectively. Among full-benefit dual eligibles qualifying for both C-SNPs and more integrated plans, those who were Black or Hispanic were more likely to enroll in C-SNPs rather than more integrated plans, which may have important implications for health equity. Policy makers should attend to these trends to ensure that both national- and state-level efforts to increase dual eligibles' enrollment in integrated plans are not significantly diluted.