Yes it is true. At the speed of light you increase to infinite mass. You can see this in a simplistic way if you rearrange Einstein's famous E=mc^2 as follows: m=E/c^2. To go the speed of light, you need huge E, much greater than c, hence m must also be huge. However, you then get into the confusion between *rest* mass and *relativistic* mass. For an exhaustive discussion of this look at "Does Mass Change with Velocity" at the Usenet Physics FAQ.
We have answered other questions about relativity and the speed of light:
As the particle's speed increases, its relativistic mass m(v) increases. To put it simply: more speed means more kinetic energy which further means more relativistic mass, hence nature keeps the relative speed less than the speed limit which is the speed of light. If we keep on adding energy to the particle, the speed will be maintained within the speed limit by radiating energy in the form of electromagnetic radiation.