The council made the decision following independent legal advice which said that to require the chief executive to speak Welsh when appointed would constitute unlawful, indirect discrimination under the Race Relations Act 1976.
A statement from the council says: 'The Welsh language is a vibrant, valued and important aspect of the community in Carmarthenshire and, if the new chief executive is not a Welsh speaker, the council will require the new chief executive to learn Welsh to a specified standard within two years.'
The Commission for Racial Equality and the Welsh Language Board have issued guidance on the issue which says linguistic requirements could cause indirect discrimination if they distinguish between racial groups.
Leader Meryl Gravell (Ind) said: 'It is absolutely critical that Carmarthenshire CC is able to recruit the best person for this post and if they do not already speak Welsh the authority is committed to providing the support and training needed to enable them to learn the language.'
Alistair Robertson, honorary secretary of the Association of Local Authority Chief Executives, said: 'This is built into the terms and conditions so it could lead to a breach of contract and would negate a claim for unfair dismissal.
'We are sympathetic to the right cultural approach but this could restrict candidates to a very small pool in a very demanding area.'