Main inclusion criteria:  Diagnosis of CHE, defined as hand eczema that has persisted for more than 3 months or returned twice or more within the last 12 months. Disease severity graded as moderate to severe at screening and baseline according to IGA-CHE (i.e. an IGA-CHE score of 3 or 4). HESD itch score (weekly average) of ≥4 points at baseline. Participants who have a documented recent history of inadequate response to treatment with topical corticosteroids (TCS) or for whom TCS are documented to be otherwise medically inadvisable (e.g. due to important side effects or safety risks). Participants adherent to standard non-medicated skin care including avoidance of known and relevant irritants and allergens.  Main exclusion criteria:  Concurrent skin diseases on the hands, e.g. tinea manuum. Active atopic dermatitis requiring medical treatment in regions other than the hands and feet. Active psoriasis on any part of the body. Hyperkeratotic hand eczema in combination with a history of psoriasis on any part of the body. Clinically significant infection on the hands. Systemic treatment with immunosuppressive drugs, immunomodulating drugs, retinoids, or corticosteroids within 28 days prior to baseline. Use of tanning beds, phototherapy, or bleach baths on the hands within 28 days prior to baseline. Previous or current treatment with Janus kinase (JAK) inhibitors (including delgocitinib/LEO 124249), systemic or topical. Cutaneously applied treatment with immunomodulators or TCS on the hands within 14 days prior to baseline. Use of systemic antibiotics or cutaneously applied antibiotics on the hands within 14 days prior to baseline. Other transdermal or cutaneously applied therapy on the hands (except for the use of subject's own emollients) within 7 days prior to baseline. Cutaneously applied treatments in regions other than the hands, which could interfere with clinical trial evaluations or pose a safety concern within 7 days prior to baseline.  Treatment with any marketed biological therapy or investigational biologic agents:  Any cell-depleting agents: within 6 months prior to baseline, or until lymphocyte count returns to normal, whichever is longer. Other biologics: within 3 months or 5 half-lives, whichever is longer, prior to baseline. Clinically significant infection within 28 days prior to baseline which, in the opinion of the investigator, may compromise the safety of the participant in the trial, interfere with evaluation of the IMP, or reduce the participant's ability to participate in the trial. History of any known primary immunodeficiency disorder including a positive human immunodeficiency virus (HIV) test at screening, or the participant taking antiretroviral medications as determined by medical history and/or participant's verbal report.  Any disorder which is not stable and could:  Affect the safety of the participant throughout the trial. Impede the participant's ability to complete the trial. Positive hepatitis B surface antigen or hepatitis C virus antibody serology at screening.