This paper presents an experimental test of the theory of individual sense of fairness of Karni and Safra (2000). According to this theory individuals' choice among random procedures designed to allocate indivisible goods is motivated, in part, by concern for fairness. The experimental study is intended to test this hypothesis. In the experiments, the subjects are asked to play a three person dictator game. The dictator, player A, is presented with a feasible set of lotteries that assign to each player a probability of winning a \$15 prize. Player A is asked to choose a lottery from the feasible set (i.e. a point along a chord in the two-dimensional probability simplex) to be used in actually allocating the prize. The feasible set is constructed such that by giving up some of his own probability of winning the prize, player A can make the overall lottery more ``fair''. If these subjects have no concern for fairness, they will choose the lottery that assigns them the highest probability of winning. However, if they have preference for fairness, they may choose a lottery farther down the chord thereby trading off some of their own chance of winning for a fairer allocation procedure. The results indicate strongly bi-modal outcomes with around half of the subjects keeping the initial allocation which yields the highest probability of winning for the dictator while the other half chooses very close to the ``perfect equity'' point along the chord. Several other properties of the subjects' preferences are also checked such as whether or not their preferences are symmetric with respect to the other players, the impact of endowment effects on preferences for fairness and the notion of fairness that underlies their choices.