  We state strong Marstrand properties for two related families of fractals in
Heisenberg groups $\mathcal{H}^d$: limit sets of Schottky groups in good
position, and attractors of self-similar IFS enjoying the open set condition in
the quotient $\mathcal{H}^d/Z$. For such a fractal $X$, we show that the
dimension of $\pi_x X$ does not depend on $x \in \mathcal{H}^d$, where $\pi_x$
denotes the radial projection along chains passing through $x$. This follows
from a local entropy averages argument due to Hochman and Shmerkin.
