The letter was signed by him in his capacity as chairman of the committee.

in 在这里表示"处于某种状态或身份"。 his 是代词 he 的所有格形式，表示"他的"。 capacity 本义是"容量、能力"，在这里引申为"身份、职位"。 as 在这里表示"作为、以...的身份"。 in his capacity as 是一个固定搭配，表示"以...的官方身份"，强调某人行使的是正式职务赋予的权力或职责。