Chiral cosmic strings naturally arise in many particle physics models, in p
articular in supersymmetric theories with a D-term. These strings have a si
ngle fermion zero mode in the core. We derive the general equation of motio
n for such strings. In Minkowski space we give the self-intersections for a
n arbitrary varying current on the loop, showing that the self-intersection
probability is dominated by the fraction of loop with maximal charge. We s
how how to relate the charge to the fermion condensation temperature, argui
ng that strings which become current carrying at formation will automatical
ly have a maximal charge. Any daughter loops produced are likely to have th
e same charge as the parent loop. Possible models for chiral cosmic strings
are also discussed and consequences for D-term inflation mentioned. (C) 20
01 Elsevier Science B.V. All rights reserved.