In the movie Into the Storm (2014) near the end, storm chaser Pete sees the eye of a massive tornado.

In 1928 (real life), Will Keller was in his barn when a huge tornado passed through. He reported seeing an opening in the center of the tornado "about 55 feet (17 meters) across and extended some 2,500 feet (762 meters) up." Source

Is there any "official" documentation or evidence that tornadoes, especially stronger ones, have eyes like a hurricane does? Or is it just an urban legend?

• Theoretically, the eye of the storm is the center of the tornado in which everything is peaceful and calm. It has been described as "still as death." I was trapped in an F-1 tornado near my home in Philadelphia and saw the eye. Everything was extremely peaceful and it was as if the storm had passed. It was dark and eerily calm. But in no time, the trailing winds hit and the the back end winds were a bit stronger than the initial ones. Hope this helps! – user5370 Feb 1 '16 at 14:00
• Hi Jeff, welcome to Earth Science. Although your experience is interesting, we are looking for science-based answers rather than personal anecdotes. I have converted your answer to a comment. Once you have 50 reputation, you will be able to comment everywhere! – gerrit Feb 2 '16 at 11:35

$$\dfrac{v^2}{r} = -\dfrac{1}{\rho}\dfrac{\partial p}{\partial n}$$
where centripetal force balances radial pressure gradient. Here, $v$ is tangential wind speed, $r$ distance from vortex center, $\rho$ is air density, $p$ is atmospheric pressure and $n$ is the radial direction pointing inward. From here, tangential wind speed is simply:
$$v = \sqrt{-\dfrac{r}{\rho}\dfrac{\partial p}{\partial n}}$$
suggesting that $v\to0$ when $r\to0$. While the flow in tornadoes is highly non-stationary and subject to friction, this idealized model shows why there must exist an "eye" inside a vortex or an area of closed circulation. This "eye" may or may not be easily recognized by a hypothetical human observer inside a tornado.