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Recent advances in Neural Radiance Fields (NeRF) boast impressive performances for generative tasks such as novel view synthesis and 3D reconstruction. Methods based on neural radiance fields are able to represent the 3D world implicitly by relying exclusively on posed images. Yet, they have seldom been explored in the realm of discriminative tasks such as 3D part segmentation. In this work, we attempt to bridge that gap by proposing SegNeRF: a neural field representation that integrates a semantic field along with the usual radiance field. SegNeRF inherits from previous works the ability to perform novel view synthesis and 3D reconstruction, and enables 3D part segmentation from a few images. Our extensive experiments on PartNet show that SegNeRF is capable of simultaneously predicting geometry, appearance, and semantic information from posed images, even for unseen objects. The predicted semantic fields allow SegNeRF to achieve an average mIoU of $\textbf{30.30%}$ for 2D novel view segmentation, and $\textbf{37.46%}$ for 3D part segmentation, boasting competitive performance against point-based methods by using only a few posed images. Additionally, SegNeRF is able to generate an explicit 3D model from a single image of an object taken in the wild, with its corresponding part segmentation.