Final answer:
The most likely service that would impair independence under the AICPA Code of Professional Conduct when assisting with the implementation of a new computer system for a privately held audit client is performing a search for and hiring new personnel.
Step-by-step explanation:
The auditor's independence might be impaired when providing certain non-audit services to their audit client, as outlined in the AICPA Code of Professional Conduct. In this case, the most likely service that would impair independence is performing a search for and hiring new personnel to operate the new computer system (option B). This directly involves the auditor in management's decision-making process, which can compromise their objectivity and independence. It is important for auditors to maintain independence to ensure the integrity and credibility of their audits.