the statement is false. Here are two counter-examples:
1. Just as ksr985 said, a compound can be meso, which would mean that the net optical activity is zero. (Really? What if you have (R*,S*)-2-bromo-3-chloro-butane? Hmm)
2. You can also have a funky situation where two carbons form a cage compound. Think of butane. Now, think of carbons two and three. Imagine us splitting the bond between the two apart and inserting tow carbons such that the resulting figure is a square where carbons two and three are at entirely opposite ends. Now add two didfferent substituents to carbons one and four, and you have carbon two and three being chiral, but the overall compound can have no optical activity. At least I think ...