The Belarus-American (BelAm) Thyroid Study cohort consists of persons 0–18 years of age at the time of exposure to radioiodines from the 1986 Chernobyl nuclear power plant accident who have undergone serial thyroid screenings with referral for fine-needle aspiration biopsy (FNAB) using standardized criteria. We investigated thyrocyte nuclear abnormalities in cytological samples from FNABs in 50 BelAm subjects with thyroid nodules and 43 control patients from Leningrad, Russia, unexposed to Chernobyl fallout. Nuclear abnormalities such as internuclear chromosome bridges and derivative nuclei with broken bridges (i.e., “tailed” nuclei), formed from dicentric and ring chromosomes, may be cellular markers of radiation exposure. In the exposed BelAm cohort, thyrocytes with bridges were present in 80% of subjects with single-nodular goiters compared with 27% of unexposed controls. The average frequency of thyrocytes with bridges was also significantly higher in the BelAm subjects than in controls as was the mean frequency of thyrocytes with tailed nuclei. In the case of multi-nodular goiters, thyrocytes with bridges were present in 75.0% of exposed BelAm patients compared with 16.7% of unexposed controls. Thyrocytes with tailed nuclei were observed in all of the BelAm subjects but in only 35% of controls, and the mean frequency of tailed nuclei was significantly higher. Unusually long bridges were detected in 29% of BelAm patients with single-nodular goiters and 35% of cases with multi-nodular goiters, while no such abnormalities were observed in the follicular thyroid epithelium of patients from the Leningrad region. Further study is needed to understand whether these phenomena represent irradiation consequences in the human organism.