I hadn’t heard of this name until a couple of years ago, but I now know two girls with this name. However, they pronounce it differently. [name]One[/name] girl pronounces it [name]Ca[/name]-LISS-ta, and the other pronounces it [name]Ca[/name]-[name]LEE[/name]-sta. I personally prefer the second pronunciation, but I am curious as to what the proper of traditional pronunciation is. The girl who pronounces it [name]Ca[/name]-[name]LEE[/name]-sta is of Greek ethnic background, but she was born in [name]Canada[/name], and since [name]Calista[/name] is an ancient Greek name, it would seem more likely to be pronounced correctly with her, but you never know. Also, is it traditionally spelled [name]Calista[/name] or [name]Callista[/name]?
Traditionally, I believe it’s spelled [name]Calista[/name], although I do have a certain fondness for [name]Callista[/name], too. I’ve always heard it with the “liss” sound, but I suppose it could be cah-lee-sta. Everywhere I looked, forvo, btn, ingolo, even babynamesworld (whose database I usually trust) all list it as having the “liss” sound in the middle. @dantea has a Greek mythology name guide post (Nameberry - Welcome to the Nameberry Forums), and [name]Callisto[/name] she lists as cah-LISS-toe (and she knows her Greek!), so I would assume it was cah-LISS-tah. Pretty name, regardless. 
^ That’s the precise thread I was digging for, [name]Ashley[/name] beat me to it 
Agreed that I’ve only heard [name]Calista[/name] as cah-LISS-tah (or, more accurately to my dialect, cuh-LISS-tuh).