It is difficult to answer this question for your particular case as there are quite a few factors that can affect the answer, including how much time has elapsed since the charge was made and the company's policy regarding refunds. Even the number of other customers that are complaining and/or disputing charges can affect the outcome.
In general, most companies will issue a refund if you simply request it from them and explain why you are dissatisfied with their service. I always recommend everyone attempt this method first since it is the simplest and fastest solution. If you try that and they ignore you, or refuse to refund, then you can try a chargeback with the CC. Typically when that happens the credit card issuer will request documentation from you, and whether or not the chargeback is successful greatly depends on whether the merchant chooses to fight it. Many companies don't respond to the CC inquiry and typically the "judgement" is ruled in the purchaser's favor. If the merchant chooses to fight it though, the contract you signed is certainly going to be considered by the arbiter. IMHO fair arbitration would consider what the service is, what the merchant's cost to provide the service is, and how difficult the contract is to understand, but I can't promise that CC arbitration works that way.
In my personal experience with providing a service and accepting CC as payment, I have never disputed a chargeback, even though I'm fairly certain I could win if I elected to fight it. My reasoning for not disputing it is simply that I want all of my customers to be happy, and if they aren't for some reason, then I feel a refund is fair.