Inclusion Criteria:  Age >18 years Written informed consent  Histologically confirmed diagnosis of CD30-expressing PTCL. The following histological subtypes according to the Revised European-American Lymphoma World Health Organization (WHO) 2016 classification are eligible:  Systemic anaplastic large cell lymphoma (ALCL) ALK+ with age-adjusted international prognostic index (aaIPI) ≥1 Systemic anaplastic large cell lymphoma (ALCL) ALK- Peripheral T-cell lymphoma not otherwise specified (PTCL-NOS) Angioimmunoblastic T-cell lymphoma (AITL) Adult T-cell leukaemia/lymphoma (ATLL; acute and lymphoma types only, must be positive for human T cell leukaemia virus 1) Enteropathy-associated T-cell lymphoma (EATL) Hepatosplenic T-cell lymphoma Monomorphic epitheliotropic intestinal T-cell lymphoma (MEITCL) Indolent T-cell lymphoproliferative disorder (T-LPD) of the gastrointestinal (GI) tract Follicular T-cell lymphoma Nodal peripheral T-cell lymphoma with T-follicular helper (TFH) phenotype Positive CD30 expression by local pathology assessment. Patients must have at least one measurable disease site. The lesion must be fluorodeoxyglucose (FDG)-avid by PET and must have a greatest transverse diameter of ≥1.5 cm and greatest perpendicular diameter of ≥1.0 cm by CT, as assessed by the site radiologist. Eastern Cooperative Oncology Group (ECOG, Appendix B) performance status of 0 to 1 Patient must be autologous stem cell transplant (ASCT)-eligible Patient must be appropriate candidate for treatment with anthracyclines  Patient must have the following laboratory criteria at screening:  Absolute neutrophil count (ANC) ≥ 1.0 x 109/L (unless secondary to bone marrow involvement by PTCL) Platelet count ≥ 50 x 109/L (unless secondary to bone marrow involvement by PTCL) Total serum bilirubin < 1.5 × upper limit of normal (ULN) unless secondary to Gilbert's syndrome or documented liver involvement by lymphoma. Patients with Gilbert's syndrome or documented liver involvement by lymphoma may be included if their total bilirubin is ≤3 × ULN Alanine transaminase (ALT), aspartate aminotransferase (AST) and alkaline phosphatase (ALP) ≤3 × ULN, or <5 × ULN in cases of documented liver involvement by lymphoma Serum creatinine clearance must be >40 mL/minute/1.73m2 either measured or calculated using a standard Cockcroft and Gault formula (Cockroft and Gault, 1976, Appendix A) and serum creatinine must be <175 µmol/L. Females of childbearing potential (FCBP) must not be pregnant or breastfeeding and must agree to use at least two effective contraception method during the study and for 6 months following the last dose of treatment. Male participants must: Males who have partners of childbearing potential must agree to use an effective contraceptive method during the study and for 6 months following the last dose of treatment.  In the opinion of investigator, the patient must:  be able to understand, give written informed consent, and comply with all study-related procedures, medication use, and evaluations not have a history of noncompliance in relation to medical regimens or be considered potentially unreliable and/or uncooperative  Exclusion Criteria:  Current diagnosis of any following lymphomas:  Primary cutaneous CD30-positive T-cell lymphoproliferative disorders and lymphomas. Cutaneous ALCL with extracutaneous tumour spread beyond locoregional lymph nodes is eligible (previous single-agent treatment to address cutaneous and locoregional disease is permissible) Mycosis fungoides (MF), including transformed MF PTCL CD30-negative History of another primary invasive cancer, hematologic malignancy, or myelodysplastic syndrome that has not been in remission for at least 3 years. Exceptions are malignancies with a negligible risk of metastasis or death (e.g., 5-year OS ≥90%), such as carcinoma in situ of the cervix, non- melanoma skin carcinoma, localized prostate cancer, ductal carcinoma in situ, or Stage I uterine cancer. History of progressive multifocal leukoencephalopathy (PML). Known central nervous system (CNS) lymphoma involvement Prior treatment with brentuximab vedotin. Baseline peripheral neuropathy ≥Grade 2 (per the NCI CTCAE, Version 5.0) Left ventricular ejection fraction (LVEF) of < 45% or history of myocardial infarction ≤6 months, or symptomatic cardiac disease (including symptomatic ventricular dysfunction, symptomatic coronary artery disease, and symptomatic arrhythmias) or prior treatment with anthracyclines. Any uncontrolled Grade 3 or higher (per the National Cancer Institute's Common Terminology Criteria for Adverse Events, NCI CTCAE Version 5.0) viral, bacterial, or fungal infection within 2 weeks prior to the first dose of study treatment. Known human immunodeficiency virus (HIV) infection, hepatitis B surface antigen-positive status, or known or suspected active hepatitis C infection. History of hypersensitivity to any component of CHEP, to compounds of similar biological or chemical composition as brentuximab vedotin, and/or the excipients contained in any of the drug formulations of study treatment. Females who are pregnant or breastfeeding Planned CNS prophylaxis with intravenous high-dose methotrexate.