The dispute relates to the claim of songwriting legend Seth Swirsky and his partner Warryn Campbell that they came up with the tune.
Two years ago, a judge dismissed the lawsuit Swirsky filed against Carey, but an appeals court now says Swirsky and his partner can go ahead and sue.
"When I first heard her song on the radio, I pulled over to the side of the road, and I just couldn't believe what I was hearing," Swirsky said. "It was my song. I have to defend my songs. My songs are like my children."
A jury will now decide who is right.