There's no reason to expect far-flung corners of the universe to have different chemistry. We already know what the periodic table is for those unexplored regions of space, and they don't have anything cheaper and more versatile than carbon.

Maybe I'm underestimating the field, but I suspect there is still a lot to learn about chemistry in extreme environments (ultra hot, dense, etc), which would be most of the universe. Some experimentation is possible on Earth, but how much could we really learn about, say, liquid water if all we could produce were a few molecules in very restricted environments? I guess that's all kind of irrelevant until we're ready to try building transistors inside the Sun.

We already know enough about chemistry and physics to rule out the possibility of building transistors inside the sun, or any other useful permanent structure inside a star. At the opposite end of the spectrum, we're already commercially exploiting temperatures on par with deep space and extremely low pressures. Yes, there's a lot we don't know about the properties of things or conditions that are hard to keep around in large quantities in the lab. But we're not going to discover complex life or be able to engineer complex and cost-effective machines in conditions where there's so much energy that molecular bonds can't stay intact or where there's so little energy that nothing gets done at better than a glacial pace. There's surely interesting stuff left to be discovered in those fields, but we won't magically stumble across a plasma-based computing substrate that is better than what we can already do on Earth.

I'm not this confident on our knowledge of the high pressure environments inside stars.

We can rule-out unexpected simple chemistry on other planets and in the outer space, but the inside of stars is too different an environment.

Also, we surely can not rule-out anything from complex chemistry on any kind of environment. Macromolecules and non-repeating crystals are very badly understood.

We were also quite sure at one point that the earth was flat.

Asimov's response: http://chem.tufts.edu/answersinscience/relativityofwrong.htm

It is rather easy to collect sufficient evidence to conclude that the earth is not flat. The people who thought the earth was flat put very little effort into determining the shape of the earth.

Modern scientists have put a great deal of effort into determining the fundamental laws of physics. They have done a proper job of looking for evidence that the laws of physics can vary with location, and they've found none.

The most obvious check would be to go somewhere else and run some experiments. We have not done that.

Seeing as we're limited by the number of protons that can hold themselves together, I'm pretty sure we can discover most things here... at least in theory.