The cha-cha dance is a dance that originated from Cuba and was originally known as the cha-cha-cha. The dance gained popularity around the 1950's and was created from two other dances – the 'mambo' and the 'danzon'. While working with the charanga group 'Orquesta America' in Cuba to perform at dance halls in Havana, Enrique Jorrin, a violinist and composer, realized that most of the crowds related the danzon-mambo rhythm to a much slower mambo dance and thus had hardship adopting the syncopated rhythms.
He decided to compose music that strongly focused on the first downbeat such that the rhythm became less syncopated. This caused the crowd dancers to develop a triple step, creating the sound 'cha-cha-cha' with their dancing shoes, thus the cha-cha-cha was born. Some, however, maintain that the footwork pattern one-two-cha-cha-cha has its roots in the vocal imitation of the sound produced by dance shoes in the chase which indicates that the name of the dance is basically an onomatopoeia that comes out of the sound of itsdancers shoes.
This explains why many call it the 'cha-cha-cha' and others 'cha-cha'. Other's have speculated that the name and dance originate from the ritual dances and religious music of the West Indians who used some plants which had seedpods they called cha-cha to build a musical rattle called the cha-cha for use in religious singing and thus dancing.