Paternal alcohol abuse is a well-recognized risk factor for the development of an alcohol use disorder (AUD). In addition to genetic and environmental risk factors, heritable epigenetic factors also have been proposed to play a key role in the development of AUD. However, it is not clear whether epigenetic factors contribute to the genetic inheritance in families affected by AUD. We used reciprocal crosses of the alcohol-preferring (P) and -nonpreferring (NP) rat lines to test whether epigenetic factors also impacted alcohol drinking in up to two generations of offspring. F1 offspring derived by reciprocal breeding of P and NP rats were tested for differences in alcohol consumption using a free-choice protocol of 10% ethanol, 20% ethanol, and water that were available concurrently. In a separate experiment, an F2 population was tested for alcohol consumption not only due to genetic differences. These rats were generated from inbred P (iP) and iNP rat lines that were reciprocally bred to produce genetically identical F1 offspring that remained alcohol-naïve. Intercrosses of the F1 generation animals produced the F2 generation. Alcohol consumption was then assessed in the F2 generation using a standard two-bottle choice protocol, and was analyzed using genome-wide linkage analysis. Alcohol consumption measures were also analyzed for sex differences. Average alcohol consumption was higher in the F1 offspring of P vs. NP sires and in the F2 offspring of F0 iP vs. iNP grandsires. Linkage analyses showed the maximum LOD scores for alcohol consumption in both male and female offspring were on chromosome 4 (Chr 4). The LOD score for both sexes considered together was higher when the grandsire was iP vs. iNP (5.0 vs. 3.35, respectively). Furthermore, the F2 population displayed enhanced alcohol consumption when the P alleles from the F0 sire were present. These results demonstrate that epigenetic and/or non-genetic factors mapping to rat chromosome 4 contribute to a transgenerational paternal effect on alcohol consumption in the P and NP rat model of AUD.