Inclusion Criteria:  Age ≥80 years AND/OR considered too frail for intensive/standard treatment defined by a frailty score of >2 on the FRAIL scale via the patient´s assessment. Have documented CLL requiring treatment according to iwCLL 2018 criteria Ability and willingness to provide written informed consent and to adhere to the study visit schedule and other protocol requirements Glomerular Filtration Rate (GFR) >30ml/min directly measured with 24hr urine collection, calculated according to the modified formula of Cockcroft and Gault (for men: GFR ≈ ((140 - age) x bodyweight)/ (72 x creatinine), for women x 0, 85) or an equally accurate method (Please note: Patients currently on hemodialysis are excluded from participating in the trial) Adequate liver function as indicated by a total bilirubin ≤ 3 x, Aspartate-Aminotransferase/Alanin-Aminotransferase (AST/ ALT) ≤ 3 x the institutional Upper Limit of Normal (ULN) value, unless directly attributable to the patient's CLL or to Gilbert's Syndrome  Adequate marrow function independent of growth factor or transfusion support as follows, unless cytopenia is due to marrow involvement of CLL:  Absolute neutrophil count ≥ 1.0 × 10^9/L Platelet counts ≥ 30 × 10^9/L; in cases of thrombocytopenia clearly due to marrow involvement of CLL (per the discretion of the investigator); platelet count should be ≥ 10 × 10^9/L if there is bone marrow involvement Total haemoglobin ≥ 9 g/dL (without transfusion support, unless anaemia is due to marrow involvement of CLL) Negative serological testing for hepatitis B (HBsAg negative and anti-HBc negative; patients positive for anti-HBc may be included if PCR for HBV DNA is negative and HBV-DNA Polymerase Chain Reaction (PCR) is performed every month until 12 months after last month of treatment), negative testing for hepatitis C RNA within 6 weeks prior to registration Life expectancy ≥ 3 months Maximum of 1 previous treatment for CLL  In case of a recent previous treatment, patients must have recovered from acute toxicities and treatment regimen must be stopped within the following time periods before start of the study treatment in the CLL-Frail trial:  chemotherapy ≥ 28 days antibody treatment ≥ 14 days kinase inhibitors (see also exclusion criterion 6), BCL2-antagonists or immunomodulatory agents ≥ 3 days corticosteroids may be applied until the start of the study therapy, these have to be reduced to an equivalent of ≤ 20 mg prednisolone per day during treatment Signed informed consent and, in the investigator's judgment, able to comply with the study protocol  Exclusion Criteria:  >1 prior CLL-specific therapy (except corticosteroid treatment administered due to necessary immediate intervention; within the last 14 days before start of study treatment, only dose equivalents up to 20 mg prednisolone are permitted) Transformation of CLL to aggressive Non-Hodgkin's Lymphoma (NHL) e.g. Richter's transformation or prolymphocytic leukaemia Patients with a history of confirmed progressive multifocal leukoencephalopathy (PML) Patients with uncontrolled autoimmune haemolytic anaemia or immune thrombocytopenia Prior exposure to acalabrutinib Progression during previous treatment with another BTK inhibitor, and/or presence of known mutations associated with resistance to therapy, e.g. Bruton´s Tyrosine Kinase (BTK) and Phospholipase C Gamma 2 (PLCg2) Uncontrolled concomitant malignancy, i.e. any concomitant malignancy that may compromise the assessment of CLL stage and the response assessment of the study treatment Eastern Cooperative Oncology Group Performance Status (ECOG) performance status >3 Uncontrolled or active infection (including positive SARS-Cov-2 PCR result) Patients with known infection with human immunodeficiency virus (HIV) Significant cardiovascular disease such as symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 3 months of screening, or any class 4 cardiac disease as defined by the New York Heart Association Functional Classification at Screening (Please note: Subjects with controlled, asymptomatic atrial fibrillation are allowed to enroll on study) Presence of a gastrointestinal ulcer diagnosed by endoscopy within 3 months before screening Significantly increased risk of bleeding according to the investigator´s evaluation, e.g. due known bleeding diathesis (e.g. von-Willebrandt´s disease or hemophilia), major surgical procedure ≤ 4 weeks or stroke/intracranial hemorrhage ≤ 6 months Use of investigational agents which might interfere with the study drug within 28 days prior to registration for study screening Requirement of therapy with strong CYP3A4 inhibitors/inducers or anticoagulant with phenprocoumon (marcumar) or other vitamin K-antagonists (Please note: Switch to alternative anticoagulants for vitamin K antagonists is permitted) Inability to swallow tablets Legal incapacity Prisoners or subjects who are institutionalized by regulatory or court order Persons who are in dependence to the sponsor or an investigator