  We show that the attraction-repulsion chemotaxis system \begin{equation*}
\begin{cases} u_t = \Delta u - \chi\nabla\cdot(u\nabla v_1) +
\xi\nabla\cdot(u\nabla v_2)\\
  \partial_t v_1 = \Delta v_1 - \beta v_1 + \alpha u \\
  \partial_t v_2 = \Delta v_2 - \delta v_2 + \gamma u, \end{cases}
\end{equation*} posed with homogeneous Neumann boundary conditions in bounded
domains $\Omega=B_R \subset \mathbb{R}^3$, $R>0$, admits radially symmetric
solutions which blow-up in finite time if it is attraction-dominated in the
sense that $\chi\alpha-\xi\gamma>0$.
