Depression is strongly related to social behavior. We have previously shown that social behavior of rats is individually stable. The purpose of the present study was to compare the sensitivity of animals with different sociability to chronic variable stress (CVS). Four social interaction tests were performed with 60 single-housed male Sprague–Dawley rats. Twenty rats with the lowest and 20 with the highest average social activity time were selected as low sociability (LS) and high sociability (HS) rats, respectively. Both groups were further divided into control and stress groups with equal average body weight. The CVS procedure lasted for 3 weeks. The stressors applied were cold water and wet bedding, imitation of injection, stroboscopic light, movement restriction in a small cage, tail pinch with a clothespin, and strong illumination during the predicted dark phase. In HS-rats, but not in LS-rats, CVS reduced sucrose intake compared with baseline after 3 weeks, suggesting that HS-rats are more vulnerable to anhedonia elicited by CVS. LS-animals were more anxious in the social interaction and open field tests, but stress eliminated differences with HS-animals in the social interaction test and increased their activity in the forced swimming test. In LS-rats stress increased ex vivo dopamine levels and reduced 5-HT levels in the frontal cortex, suggesting that the increased behavioral activity after stress may be related to increased impulsivity. This study thus revealed that animals with high sociability trait are more vulnerable to anhedonia elicited by chronic stress in conditions of single housing.