  We construct a double field theory coupled to the fields present in
Vasiliev's equations. Employing the "semi-covariant" differential geometry, we
spell a functional in which each term is completely covariant with respect to
$\mathbf{O}(4,4)$ T-duality, doubled diffeomorphisms, $\mathbf{Spin}(1,3)$
local Lorentz symmetry and, separately, $\mathbf{HS}(4)$ higher spin gauge
symmetry. We identify a minimal set of BPS-like conditions whose solutions
automatically satisfy the full Euler-Lagrange equations. As such a solution, we
derive a linear dilaton vacuum. With extra algebraic constraints further
supplemented, the BPS-like conditions reduce to the bosonic Vasiliev equations.
