When $\ce{HBr}$ is added to 2-chloro-2-butene, the proton preferentially bonds to the $sp^2$ carbon that's not bonded to chlorine. Does this mean that hyperconjugation takes place between the lone pairs of chlorine and the positively charged $C3$? I would assume that since there is still a free rotation about the $\ce{C-Cl}$ bond and that chlorine is in a tetrahedral formation this would be the reason behind the regioselectivity.
Hyperconjuation is the interaction of electrons in sigma orbitals (in $C-H$ or $C-C$) with an adjacent empty p orbital or $\pi$ orbital. What you are describing is not hyperconjugation, but resonance; more specifically, the chlorine shows the $+R$ effect.
Now if you draw the resonance structures of this molecule you will realize that the $C_3$ has a negative charge on it in one canonical form. This means, in the actual molecule, that $C_3$ carbon has a partial negative charge, which is why the hydrogen from $HBr$ preferentially bonds to that carbon.
A more acceptable explanation would be that, when the hydrogen bonds to $C_3$, the resultant intermediate carbocation (positive charge on $C_2$) is stabilized by the $+R$ effect of chlorine, resulting in a racemic mixture of $2-bromo-2-chlorobutane$ to form as the major product.
