  We describe a family of representations in SL(3,$\mathbb C$) of the
fundamental group $\pi$ of the Whitehead link complement. These representations
are obtained by considering pairs of regular order three elements in
SL(3,$\mathbb C$) and can be seen as factorising through a quotient of $\pi$
defined by a certain exceptional Dehn surgery on the Whitehead link. Our main
result is that these representations form an algebraic component of the
SL(3,$\mathbb C$)-character variety of $\pi$.
