  The expansion of the Universe is observed to be accelerating, with the
simplest solution being a classical cosmological constant. However, this
receives contributions from the quantum vacuum, which are predicted to be many
orders of magnitude larger than observations, and suffers from radiative
instabilities requiring repeated fine tuning. In this paper we present a
minimal, self tuning scalar field model that can dynamically cancel a large
quantum vacuum energy, avoiding Weinberg's No Go Theorem, and produce
accelerated de Sitter expansion at a lower energy scale as a solution to the
problem. Our minimal model, which contains a non canonical kinetic energy and a
linear potential, belongs to the Kinetic Gravity Braiding subclass of Horndeski
theory which is not observationally excluded, and lies outside of the known Fab
Four or Well Tempered models. We find analytic solutions in the limits of slow
roll and fast roll, and numerically solve the equations of motion to illustrate
our model. We show that the model allows for a matter dominated era, and that
the attractor solution is stable under a phase transition in the vacuum energy
density. We also consider the energy scales required to match observations. Our
model shows the existence of a wider class of successful self tuning models
than previously assumed.
