Applying techniques developed by Geanakoplos et al. (1989), this paper analyzes the gift exchange between agents with privately observed nonpaternalistic altruism. I find that gift giving between agents under private information of altruism can be analyzed as a conventional signaling game. After applying standard refinements of signaling games, I show that, over nondegenerate ranges of parameter values, private information introduces systematic biases in agents' behavior. First, agents tend to give larger gifts than under full information. Second, despite that fact that agents have no intrinsic concern for reciprocity or fairness, the more altruistic the recipient is, the more the donor exaggerates the gift size. The second finding gives rise to a new theory of reciprocity according to which private information of unconditional altruism can lead to reciprocal behavior.