In the context of forecasted climate change scenarios, the growth of forest tree species at their distribution margin is crucial to adapt current forest management strategies. Analyses of beech (Fagus sylvatica L.) growth have shown high plasticity, but easternmost beech populations have been rarely studied. To describe the response of the marginal beech population to the climate in the far east sites of its distribution, we first compiled new tree ring width chronologies. Then we analyzed climate–growth relationships for three marginal beech populations in the Republic of Moldova. We observed a relatively high growth rate in the marginal populations compared to core distribution sites. Our analyses further revealed a distinct and significant response of beech growth to all climatic variables, assessing for the first time the relationship between growth and vapor pressure deficit (VPD) which described how plant growth responds to drought. These results highlight that accumulated water deficit is an essential limiting factor of beech growth in this region. In conclusion, beech growth in the easternmost marginal population is drought-limited, and the sensitivity to VPD will need to be considered in future studies to update the forest management of other economic and ecologically important species.