A major challenge in AI is dealing with uncertain information. While probabilistic approaches have been employed to address this issue, in many situations probabilities may not be available or may be unsuitable. As an alternative, qualitative approaches have been introduced to express that one event is no more probable than another. We provide an approach where an agent may reason deductively about notions of likelihood, and may hold beliefs where the subjective probability for a belief is less than 1. Thus, an agent can believe that p holds (with probability <1); and if the agent believes that q is more likely than p, then the agent will also believe q. Our language allows for arbitrary nesting of beliefs and qualitative likelihoods. We provide a sound and complete proof system for the logic with respect to an underlying probabilistic semantics, and show that the language is equivalent to a sublanguage with no nested modalities.