。
She was elected chair of the committee.
Literal
She [topic-は] that committee's chairperson [as-に] was-chosen.
選ばれる is the passive of 選ぶ ('to choose') — appropriate when reporting that someone was selected by some unnamed group. The に here marks the role she was selected *to fill* — 'chosen as / chosen to be the chair'. This に of role/result appears all over: ~になる ('become'), ~にする ('decide on'), ~に選ばれる ('be chosen as'). The construction silently elides the actual electors, which suits situations where the choosing was collective or institutional. 議長 literally 'discussion-leader' is the standard word for chair, presiding officer, speaker (of a parliament).