Indeed, their marriage application was rejected because the Cayman Islands don't recognize equal marriage yet. They therefore decided to launch a legal challenge against the government in order to obtain the right to marry.
The Cayman Islands are a British overseas territory but have their own laws. Homosexuality was only decriminalized in 2000 and only, as The Independent reports,because the UK forced it to.
Massive respect towards Chantelle and Vickie that we will follow in their attempt to legalize marriage equality in the Cayman Islands.