The helicity of a particle is defined as the projection of a spin vector in the direction of its momentum vector,
Therefore, if a particle's spin vector points in the same direction as the momentum vector, the helicity is positive, and if they point in opposite directions, the helicity is negative. However, the helicity of a massless particle is always equal to its chirality. The helicity of a particle is a Lorentz invariant.
References
Boyd, R. N. "Spin and Helicity Related to EM and Gravitation." http://www.rialian.com/rnboyd/spin-helicity.htm.
