Gifts are important instruments for forming bonds in interpersonal relationships. Our study analyzes the phenomenon of gift contagion in online groups. Gift contagion encourages social bonds by prompting further gifts; it may also promote group interaction and solidarity. Using data on 36 million online red packet gifts on a large social site in East Asia, we leverage a natural experimental design to identify the social contagion of gift giving in online groups. Our natural experiment is enabled by the randomization of the gift amount allocation algorithm on the platform, which addresses the common challenge of causal identifications in observational data. Our study provides evidence of gift contagion: on average, receiving one additional dollar causes a recipient to send 18 cents back to the group within the subsequent 24 hours. Decomposing this effect, we find that it is mainly driven by the extensive margin -- more recipients are triggered to send red packets. Moreover, we find that this effect is stronger for "luckiest draw" recipients, suggesting the presence of a group norm regarding the next red packet sender. Finally, we investigate the moderating effects of group- and individual-level social network characteristics on gift contagion as well as the causal impact of receiving gifts on group network structure. Our study has implications for promoting group dynamics and designing marketing strategies for product adoption.