What kind of optical activity requires chirality?
The meaning of optical activity in this context is the same as usual: the ability to rotate the plane of polarized light. To have it, a molecule must be chiral.

Chirality is the absence of certain type of symmetry. Since most small molecules have that symmetry, many students get the wrong perception that chirality is a property which must be obtained by having some functional group (asymmetric center, etc.), much like having a $\ce{-COOH}$ group makes a compound an acid. This is not quite true. Not only a compound may be chiral without any chiral centers, but it can also be achiral despite having some chiral centers, as are meso compounds.