  We initiate the geometric engineering of 2d $\mathcal{N}=(0,1)$ gauge
theories on D1-branes probing singularities. To do so, we introduce a new class
of backgrounds obtained as quotients of Calabi-Yau 4-folds by a combination of
an anti-holomorphic involution leading to a Spin(7) cone and worldsheet parity.
We refer to such constructions as Spin(7) orientifolds. Spin(7) orientifolds
explicitly realize the perspective on 2d $\mathcal{N}=(0,1)$ theories as real
slices of $\mathcal{N}=(0,2)$ ones. Remarkably, this projection is
geometrically realized as Joyce's construction of Spin(7) manifolds via
quotients of Calabi-Yau 4-folds by anti-holomorphic involutions. We illustrate
this construction in numerous examples with both orbifold and non-orbifold
parent singularities, discuss the role of the choice of vector structure in the
orientifold quotient, and study partial resolutions.
