There is plenty of evidence, but it would require to change some of our cosmological models (so it's not without controversy). A physicist that has explored the issue in detail is Joao Magueijo:

https://en.wikipedia.org/wiki/Jo%C3%A3o_Magueijo

For a good review of the VSL Theories (Varying Speed of Light Theories) and the evidence behind them see http://arxiv.org/abs/astro-ph/0305457

> Supported by evidence. (And no counter-evidence is known.)

That was true for Newtonian mechanics for a long time too.