  We study standard Einstein-Maxwell theory minimally coupled to a complex
valued and self-interacting scalar field. We demonstrate that new, previously
unnoticed spherically symmetric, charged black hole solutions with scalar hair
exist in this model for sufficiently large gravitational coupling and
sufficiently small electromagnetic coupling. The novel scalar hair has the form
of a spatially oscillating ''wave packet'' and back-reacts on the space-time
such that both the Ricci and the Kretschmann scalar, respectively, possess
qualitatively similar oscillations.
