Although matter does not quite move at the constant described as "speed of light" it is still very possible for matter to move at a speed that light also moves at.
The easiest way to get matter to move at the same speed of light or even faster is to simply make light slower. After all, the constant "speed of light" is actually "speed of light in a vacuum" and not "speed of light on earth".
Researchers at the Rowland Institute for Science slowed light to 38 miles per hour in 1999, and other great results have been gotten with the slowing of light since then.
I personally don't do it very often without the help of a train or car, but matter has and does travel quite comfortably at 38 miles per hour (and somewhat faster, taking into account planets moving and all that).
So, depending on your definition on the term "speed of light" matter can indeed not reach that speed, or it quite easily can and does.