If I am correct, chips cannot get much smaller because of Heisenberg's uncertainty principle. My friend and I want to perform an experiment (which is cheap, i.e. doesn't require million-dollar equipment) which shows that if a chip is too small, it will mess up. Is there any such experiment?
I think you are right that the Heisenberg uncertainty principle is involved in the limit. I don't think we are anywhere near the Heisenberg limit. The limit we are currently approaching is that we currently compute with devices based on atoms. An atom is about 1 angstrom = .1 nm wide. We are currently making transistors that are about 22 nm wide, so we're getting close to needing to make 1 atom transistors. If we want to scale beyond that we're going to need to find ways of computing that involve storing and manipulating multiple states per atom.
The researchers that I know of in this area are Rolf Landauer, Charles H Bennett, and Seth Lloyd. (I think Charles H Bennett considers himself a computer scientist while the other two consider themselves physicists.) Richard Feynman was also very interested in this question and has a book called Feynman Lectures on Computation (which you can read about at http://quantum.quniverse.sk/buzek/zaujimave/p257_s.pdf). Also @PeterShor is an active member here and is the expert on quantum computation.
Here's a Scientific American article by Bennett and Landauer:
Here's Seth Lloyd's article in Nature: http://arxiv.org/abs/quant-ph/9908043
Here's a web page at Cambridge: http://www.sp.phy.cam.ac.uk/~SiGe/Fundamental%20Limits%20of%20Computation%20-%20Landauer%20and%20Heisenburg.html