This organism is a fungus. Eukaryotic means that the cells have a nucleus enclosing the DNA, rather than having the genetic material in the cytoplasm; this eliminates Eubacteria, as they are prokaryotes. Protists can be both uni- and multi-cellular, some have cell walls, and they can be parasitic. But only the fungi have cell walls containing chitin. This is the deciding point for placing your organism in the kingdom Fungi. Fungi are eukaryotic, multi-cellular, parasitic, and have chitin in their cell walls. The other two kingdoms you mention have a characteristic that excludes your organism.