Figure–ground assignment is thought to entail inhibitory competition between potential objects on opposite sides of a shared border; the winner is perceived as the figure, and the loser as the shapeless ground. Computational models and response time measures support this understanding but to date no online measure of inhibitory competition during figure–ground assignment has been reported. The current study assays electroencephalogram (EEG) alpha power as a measure of inhibitory competition during figure–ground assignment. Activity in the EEG alpha band has been linked to functional inhibition in the brain, and it has been proposed that increased alpha power reflects increased inhibition. In 2 experiments participants viewed silhouettes designed so that the insides would be perceived as figures. Real-world silhouettes depicted namable objects. Novel silhouettes depicted novel objects on the insides of their borders, but varied in the amount of hypothesized cross-border competition for figural status: In “Low-Competition” silhouettes, the borders suggested novel objects on the outside as well as on the inside. In “High-Competition” silhouettes the borders suggested portions of real-world objects on the outside; these compete with the figural properties favoring the inside as figure. Participants accurately categorized both types of novel silhouettes as “novel” objects and were unaware of the real world objects suggested on the outside of the High-Competition silhouettes. In both experiments, we observed more alpha power while participants viewed High- rather than Low-Competition novel silhouettes. These are the first results to show via an online index of neural activity that figure assignment entails inhibitory competition.