To determine whether a single dose of double immune checkpoint blockade (induction chemoimmunotherapy (ICIT)) adds benefit to induction single-cycle platinum doublet (induction chemotherapy (IC)) in locally advanced head and neck squamous cell carcinoma (HNSCC), patients treated with cisplatin 30 mg/m2 d1-3 and docetaxel 75 mg/m2 d1 combined with durvalumab 1500 mg fixed dose d5 and tremelimumab 75 mg fixed dose d5 (ICIT) within the CheckRad-CD8 trial were compared with a retrospective cohort receiving the same chemotherapy (IC) without immunotherapy. The endpoint of this analysis was the complete response rate (CR). A total of 53 patients were treated with ICIT and 104 patients with IC only. CR rates were 60.3% for ICIT and 40.3% for IC (p = 0.018). In the total population (n = 157), the most important predictor to achieve a CR was treatment type (OR: 2.21 for ICIT vs. IC; p = 0.038, multivariate analysis). The most diverse effects in CR rates between ICIT and IC were observed in younger (age ≤ 60) patients with HPV-positive OPSCCs (82% vs. 33%, p = 0.176), while there was no difference in older patients without HPV-positive OPSCCs (53% vs. 48%). The analysis provides initial evidence that ICIT could result in higher CR rates than IC. Young patients with HPV-positive OPSCCs may have the greatest benefit from additional immune checkpoint inhibitors.