Inspired by Barany's colourful Caratheodory theorem, we introduce a colourful
generalization of Liu's simplicial depth. We prove a parity property and
conjecture that the minimum colourful simplicial depth of any core point in any
d-dimensional configuration is d^2+1 and that the maximum is d^(d+1)+1. We
exhibit configurations attaining each of these depths and apply our results to
the problem of bounding monochrome (non-colourful) simplicial depth.