A core symptom of alcohol use disorder (AUD) is a progressively increased choice of alcohol over alternative rewards despite negative consequences. Here, we investigated choice between personalized alcohol vs. natural rewards in a laboratory setting, and compared this behavior between non-treatment-seeking heavy drinkers and light social drinkers. 30 light social drinkers (15 men drinking < 15 drinks/week and 15 women drinking < 10 drinks/week) and 30 heavy, non-treatment-seeking drinkers (drinking more than these levels; 15 women). In the Concurrent Choice Alcohol Food (CCAF) task, participants chose between individually tailored images of alcohol and snack rewards and collected points towards the respective reward. To assess cost sensitivity, points associated to the images varied so that they favored alcohol or snack, or were equal, creating three relative point levels. Choice preference for alcohol was strongly correlated with Alcohol Use Disorder Identification Test (AUDIT) scores, supporting the external validity of the choice procedure. Compared to light drinkers, heavy drinkers showed increased choice preference for alcohol, as indicated by a between-group difference in points of subjective equality, a metric that quantifies the relative point level at which alcohol and snacks were equally likely to be chosen. In both groups, choice preference strongly depended on the relative point level of alcohol compared to snacks, suggesting that responding for alcohol in heavy drinkers was sensitive to costs. Our results replicate previous findings of a relationship between self-reported alcohol use and choice preference for alcohol. We also found that choice behavior was strongly dependent on relative cost of alcohol in both groups, although price sensitivity was lower in heavy compared to light drinkers. An increased choice preference for alcohol in heavy drinkers suggests that they attribute a higher relative reinforcing value to alcohol compared to natural rewards.