The structure that immediately identifies a cell as a eukaryote is the nucleus.

Here's why:

* Nucleus: This membrane-bound organelle houses the cell's genetic material (DNA) in the form of chromosomes. Prokaryotic cells lack a true nucleus, instead having their DNA located in a region called the nucleoid, which is not enclosed by a membrane.

* Other Features: While the nucleus is the most definitive feature, eukaryotes also have other distinguishing characteristics like membrane-bound organelles (e.g., mitochondria, Golgi apparatus), a more complex internal structure, and a cytoskeleton.

So, if you see a cell with a nucleus, you know it's a eukaryote!