Large nut weight (NW) is an important target in chestnut breeding. The present study was conducted at the Nakatsugawa branch of the Gifu Prefectural Research Institute for Agricultural Technology, an important chestnut breeding site in Japan. We estimated the environmental variance components for NW by using nine cultivars/selections with three single-tree replicates for six years. The number of nuts evaluated for each tree was mostly over 100 nuts, with an average of 440 nuts. Subsequently, the dataset of average NW values for each tree was log-transformed and analyzed by ANOVA. The effects of genotype, year, and the genotype × year interactions were highly significant, whereas the tree effect was negligible. The resulting environmental variance components for the log-transformed values were as follows: variance among years = 5.2 × 10 −4 , variance among trees within genotype = 0, variance associated with the genotype × year interactions = 7.6 × 10 −4 , and residual variance = 11.2 × 10 −4 . The results suggest that tree replication is not necessary to evaluate the genotypic value of cultivars/selections or offspring in breeding and that year effect adjustment and yearly repeated measurements can effectively reduce environmental variance. The NW of 27 cultivars/ selections with potential as cross-parents was also estimated with no tree replications and via measurements repeated for three years; the results ranged from 10.7 to 47.4 g, with high broad-sense heritability (0.93) based on a three-year evaluation for the log-transformed data. Based on the environmental variance estimates, the cultivars/selections used in chestnut breeding with NW above 22.3 and 26.7 g should be selected by evaluating one tree for three years at 95% probability and selecting those having nuts of 25 and 30 g or more, respectively.