This is a 24-week study in adult participants with severe chronic hand eczema (CHE) and with a documented inadequate response to treatment with topical corticosteroids (TCS) or for whom TCS are documented to be otherwise medically inadvisable. Eligible participants will be randomised to receive topical administration of delgocitinib cream 20 mg/g, twice-daily, or oral administration of alitretinoin capsules 30 mg (with an option to reduce to 10 mg during trial conduct), once-daily. The participants will visit the clinic regularly to have the study doctor assess their CHE and to answer questions about itch, pain, CHE symptoms, and quality of life. The purpose of this trial is to compare the efficacy, health-related quality of life, and safety of delgocitinib cream and alitretinoin capsules.