  We show numerically that a rotating, harmonically trapped mixture of two
Bose-Einstein-condensed superfluids can, contrary to its single-species
counterpart, contain a multiply quantized vortex in the ground state of the
system. This giant vortex can occur without any accompanying single-quantum
vortices, may either be coreless or have an empty core, and can be realized in
a $^{87}$Rb-$^{41}$K Bose-Einstein condensate. Our results not only provide a
rare example of a stable, solitary multiquantum vortex but also reveal exotic
physics stemming from the coexistence of multiple, compositionally distinct
condensates in one system.
