Nut weight is one of the most important traits that can affect a chestnut grower's returns. Due to the long juvenile phase of chestnut trees, the selection of desired characteristics at early developmental stages represents a major challenge for chestnut breeding. In this study, we identified single nucleotide polymorphisms (SNPs) in transcriptomic regions, which were significantly associated with nut weight in chestnuts (Castanea crenata), using a genome-wide association study (GWAS). RNA-sequencing (RNA-seq) data were generated from large and small nut-bearing trees, using an Illumina HiSeq. 2000 system, and 3,271,142 SNPs were identified. A total of 21 putative SNPs were significantly associated with chestnut weight (false discovery rate [FDR] < 10-5), based on further analyses. We also applied five machine learning (ML) algorithms, support vector machine (SVM), C5.0, k-nearest neighbour (k-NN), partial least squares (PLS), and random forest (RF), using the 21 SNPs to predict the nut weights of a second population. The average accuracy of the ML algorithms for the prediction of chestnut weights was greater than 68%. Taken together, we suggest that these SNPs have the potential to be used during marker-assisted selection to facilitate the breeding of large chestnut-bearing varieties.