Contradicting Carpetsmoker's answer, let me cite the official statement on behalf of the European Commission Representation in Ireland linked from the article linked in that answer:
We note the media reports stating that in the event of a UK withdrawal from the EU, English would cease to be an official language of the EU.
This is incorrect. The Council of Ministers, acting unanimously, decide on the rules governing the use of languages by the European institutions. In other words, any change to the EU Institutions' language regime is subject to a unanimous vote of the Council, including Ireland.
That is, while it is true that any country can only introduce one language into the list of official EU languages, languages are not dropped from the list automatically. Removing a language from the list requires every EU member to agree on it, which is unlikely to happen.