Can sp2 hybridised carbon show chirality?
As correctly stated in a comment by @Ivan Neretin, chirality is not bound to stereogenic centers (e.g. the textbook examples of carbon atoms with four different substitutents, or chiral sulfoxides) only.

Returning to your question, an other option to build chirality is of course axial chirality, where the allenes -- formally built from $sp^2$-hybridized carbon atoms -- offer enantiomeric forms.


(source)