Independence, impartiality, and the existence of an environment devoid of bias are key elements that define the integrity of any dispute resolution process. The absence of these key elements in any dispute resolution process cast doubt on due process notwithstanding the formality adopted in such process. Like every dispute resolution process, it is an ideal and a requirement in the arbitral process for every arbitrator to be impartial and independent. Arbitrators are obliged to disclose circumstances that may cast doubt on their impartiality upon acceptance of the arbitration and during the arbitration. This requirement is explicitly contained in most institutional arbitration rules and in most country’s arbitration rules. The requirement for arbitrators to disclose circumstances that may give rise to their partiality is opaque and uncertain. In the case of Halliburton v. Chubb, the English Supreme Court pronounced on the impact of the acceptance of multiple appointments by arbitrators in arbitration with the related subject matter and on the corresponding duty of an arbitrator to disclose. This article analyses the arbitrator’s duty of independence and impartiality considering the decision rendered in Halliburton v. Chubb and critically examines the arbitrator’s acceptance of multiple appointments with a related subject matter or common party, the appearance of bias, unconscious bias, and the duty of disclosure.