From Youtube: Miriam Makeba pronounces the alphabet in click sounds. Click consonants are frequent in her native Xhosa language, and she sings a song that uses them, 'Baxabene Oxamu.'
From Wikipedia: "Xhosa is spoken as a first language by approximately 8.2 million people and by another 11 million as a second language in South Africa. It has perhaps the heaviest functional load of click consonants in a Bantu language, with one count finding that 10% of basic vocabulary items contained a click." It's a written language that uses the Roman alphabet.