  In this note we prove an existence and uniqueness result of solution for
multidimensional delay differential equations with normal reflection and driven
by a H\"older continuous function of order $\beta \in (\frac13,\frac12)$. We
also obtain a bound for the supremum norm of this solution. As an application,
we get these results for stochastic differential equations driven by a
fractional Brownian motion with Hurst parameter H $\in (\frac13,\frac12)$.
