Does the Python 3 interpreter have a JIT feature?

First off, Python 3(.x) is a language, for which there can be any number of implementations. Okay, to this day no implementation except CPython actually implements those versions of the language. But that will change (PyPy is catching up).

To answer the question you meant to ask: CPython, 3.x or otherwise, does not, never did, and likely never will, contain a JIT compiler. Some other Python implementations (PyPy natively, Jython and IronPython by re-using JIT compilers for the virtual machines they build on) do have a JIT compiler. And there is no reason their JIT compilers would stop working when they add Python 3 support.

But while I'm here, also let me address a misconception:

Usually a JIT compiler is the only thing that can improve performances in interpreted languages

This is not correct. A JIT compiler, in its most basic form, merely removes interpreter overhead, which accounts for some of the slow down you see, but not for the majority. A good JIT compiler also performs a host of optimizations which remove the overhead needed to implement numerous Python features in general (by detecting special cases which permit a more efficient implementation), prominent examples being dynamic typing, polymorphism, and various introspective features.

Just implementing a compiler does not help with that. You need very clever optimizations, most of which are only valid in very specific circumstances and for a limited time window. JIT compilers have it easy here, because they can generate specialized code at run time (it's their whole point), can analyze the program easier (and more accurately) by observing it as it runs, and can undo optimizations when they become invalid. They can also interact with interpreters, unlike ahead of time compilers, and often do it because it's a sensible design decision. I guess this is why they are linked to interpreters in people's minds, although they can and do exist independently.

There are also other approaches to make Python implementation faster, apart from optimizing the interpreter's code itself - for example, the HotPy (2) project. But those are currently in research or experimentation stage, and are yet to show their effectiveness (and maturity) w.r.t. real code.

And of course, a specific program's performance depends on the program itself much more than the language implementation. The language implementation only sets an upper bound for how fast you can make a sequence of operations. Generally, you can improve the program's performance much better simply by avoiding unnecessary work, i.e. by optimizing the program. This is true regardless of whether you run the program through an interpreter, a JIT compiler, or an ahead-of-time compiler. If you want something to be fast, don't go out of your way to get at a faster language implementation. There are applications which are infeasible with the overhead of interpretation and dynamicness, but they aren't as common as you'd think (and often, solved by calling into machine code-compiled code selectively).

The only Python implementation that has a JIT is PyPy. Byt - PyPy is both a Python 2 implementation and a Python 3 implementation.

The Numba project should work on Python 3. Although it is not exactly what you asked, you may want to give it a try:https://github.com/numba/numba/blob/master/docs/source/doc/userguide.rst.

It does not support all Python syntax at this time.