  We report an unexpected theoretical discovery of a spin one half matter field
with mass dimension one. It is based on a complete set of eigenspinors of the
charge conjugation operator. Due to its unusual properties with respect to
charge conjugation and parity it belongs to a non standard Wigner class.
Consequently, the theory exhibits non-locality with (CPT)^2 = - I. Its dominant
interaction with known forms of matter is via Higgs, and with gravity. This
aspect leads us to contemplate it as a first-principle candidate for dark
matter.
