We introduce the $\theta$-twistor which is a new supersymmetric generalization of the Penrose twistor and is also alternative to the supertwistor. The $\theta$-twistor is a triple of { \it spinors} including the spinor $\theta$ extending the Penrose's double of spinors. Using the $\theta$-twistors yields an infinite chain of massless higher spin chiral supermultiplets $({ 1/2},1), (1, { 3/2}), ({ 3/2},2),...,(S, S+{ 1/2})$ generalizing the known scalar $(0,{ 1/2})$ supermultiplet
Categories: math-ph gr-qc math.MP math.SG