Recommending packages of items to groups of users has several applications, including recommending vacation packages to groups of tourists, entertainment packages to groups of friends, or sets of courses to groups of students. In this paper, we focus on a novel aspect of package-to-group recommendations, that of fairness. Specifically, when we recommend a package to a group of people, we ask that this recommendation is fair in the sense that every group member is satisfied by a sufficient number of items in the package. We explore two definitions of fairness and show that for either definition the problem of finding the most fair package is NP-hard. We exploit the fact that our problem can be modeled as a coverage problem, and we propose greedy algorithms that find approximate solutions within reasonable time. In addition, we study two extensions of the problem, where we impose category or spatial constraints on the items to be included in the recommended packages. We evaluate the appropriateness of the fairness models and the performance of the proposed algorithms using real data from Yelp, and a user study.