Are the following mutually consistent (relative to large cardinals)?
(1) There are no $\omega_2$-Aronszajn trees.
(2) There is an $\omega_1$-Kurepa tree.
In the models I know of the tree property at $\omega_2$, it also holds that there are no weak Kurepa trees on $\omega_1$ (also called Canadian trees).