The really quick answer is "maybe" – it depends on what you mean by "Arduino" and what you mean by "thread." The answer is likely to be different for the AVR based Arduinos (Uno et al.) vs. the ARM based Arduinos (Due et al.) – I would expect there to be much better hardware support for "real" threads on the ARM processors. Another question you'd want to answer is "why threads?" Do you want the abstraction to help you organize your code? Or do you actually need "real" threads?
Before there was hardware thread support (e.g., the mid-80s) there are user thread implementations, it seems possible that they might be adaptable to run even on an AVR. I would expect it to be something of a project.
There is a threads package called Protothreads which may be interesting. The description says "Protothreads are extremely lightweight stalkless threads designed for severely memory constrained systems." I found another question asking about simple usage of Protothreads, so it seems that you may find some other users of the package.
You may also find some useful information in this Stack Exchange question on threads, a quick search for "C user threads" found this implementation on the first page – and I'm sure there are many more.
A search on "Arduino threads" found several more interesting looking links:
If you just want threads, a small and inexpensive board, and I/O pins it might be worth considering a Raspberry Pi – Linux has thread support.