  We prove a version of Carleson's Theorem in the Walsh model for vector-valued
functions: For $1<p< \infty$, and a UMD space $Y$, the Walsh-Fourier series of
$f \in L ^{p}(0,1;Y)$ converges pointwise, provided that $Y$ is a complex
interpolation space $Y=[X,H]_\theta$ between another UMD space $X$ and a
Hilbert space $H$, for some $\theta\in(0,1)$. Apparently, all known examples of
UMD spaces satisfy this condition.
