BACKGROUND: Symptomatic hand osteoarthritis is more common in women than in men, and its incidence increases around the age of menopause, implicating oestrogen deficiency. No randomised controlled trials of hormone replacement therapy (HRT) have been done in people with hand osteoarthritis. We aimed to determine the feasibility and acceptability of a form of HRT (conjugated oestrogens plus bazedoxifene) in post-menopausal women with painful hand osteoarthritis. METHODS: The HOPE-e feasibility study was a randomised, double-blind, placebo-controlled trial, for which we recruited women aged 40-65 years, for whom 1-10 years had passed after their final menstrual period, with definite hand osteoarthritis and at least two painful hand joints. Participants were recruited across three primary or secondary care sites and from the community and were randomly assigned (1:1) to receive conjugated oestrogens plus bazedoxifene or placebo, orally once every day for 24 weeks, before weaning for 4 weeks until the end of the study. The primary feasibility outcomes were rates of identification, recruitment, randomisation, retention, and compliance of eligible participants, and the likelihood of unmasking. The secondary objective was to generate proof-of-concept quantitative and qualitative data on the acceptability of proposed clinical outcomes for a full trial and adverse events. We used an intention-to-treat analysis, and criteria for progression to a full trial were pre-defined as recruitment of at least 30 participants across all sites in 18 months; a dropout rate of less than or equal to 30% of randomised individuals; and acceptability to the majority of participants, including acceptable rates of adverse events. Due to the COVID-19 pandemic, the recruitment window was reduced to 12-15 months. A proportionately reduced minimum sample size of 22 was judged to be sufficient to test feasibility. This trial was registered at ISRCTN, ISRCTN12196200. FINDINGS: From May 9, 2019 to Dec 31, 2020, 434 enquiries or referrals were received. We did 96 telephone pre-screens; of the 35 eligible participants, seven were excluded as ineligible at the telephone or face-to-face screening and 28 (80% [95% CI 63-92]) were randomly assigned. Of the 406 who were not randomly assigned, 250 (62%) were ineligible (with contraindicated medications accounting for 50 [20%] of these), 101 (25%) did not respond to further enquiries, and 55 (14%) chose not to proceed (with the most common reason being not wanting to take a hormone-based drug). All 28 randomised participants completed all follow-up assessments with high compliance and outcome measure completeness. All three adverse event-related treatment withdrawals were in the placebo group. No serious adverse events were reported. Participants and investigators were successfully masked (participant Bang's blinding index placebo group 0·50 [95% CI 0·25-0·75]). The trial met the prespecified criteria for progression to a full trial. INTERPRETATION: This first-ever feasibility study of a randomised controlled trial of HRT for post-menopausal women with painful hand osteoarthritis met its progression criteria, although it was not powered to detect a clinical effect. This outcome indicates that a full trial of an HRT in this population is feasible and acceptable and identifies potential refinements with regard to the design of such a trial. FUNDING: Research for Patient Benefit programme, National Institute for Health Research.