H-4 child of a domiciled H-1B parent Yes — by published rule
Alien may establish residence unless the INA precludes domicile. UC/CSU eligible charts: A, E, G, H-1(B), H-4, I, K, L, N-8/9, NATO, O-1/O-3, R, T, U, V (E-3 at CSU; P needs confirming). Status must be held 1+ year before the residence determination date. Ineligible: B, C, D, F, H-2/H-3, J, M, P (CSU), Q, TN/TD.