  We construct local models for wildly ramified unitary similitude groups of
odd dimension $n\geq 3$ with special parahoric level structure and signature
$(n-1,1)$. We first give a lattice-theoretic description for parahoric
subgroups using Bruhat-Tits theory in residue characteristic two, and apply
them to define local models following the lead of Rapoport-Zink and
Pappas-Rapoport. In our case, there are two conjugacy classes of special
parahoric subgroups. We show that the local models are smooth for the one class
and normal, Cohen-Macaulay for the other class. We also prove that they
represent the v-sheaf local models of Scholze-Weinstein. Under some additional
assumptions, we obtain an explicit moduli interpretation of the local models.
