  Mixed halide chemistry has recently been utilized to tune the intrinsic
magnetic properties of transition-metal halides $-$ one of the largest families
of magnetic van der Waals materials. Prior studies have shown that the strength
of exchange interactions, hence the critical temperature, can be tuned smoothly
with halide composition for a given ground-state. Here we show that the
ground-state itself can be altered by a small change of halide composition
leading to a quantum phase transition in FeCl$_{3-x}$Br$_x$. Specifically, we
find a three-fold jump in the N\'{e}el temperature and a sign change in the
Weiss temperature at $x= 0.08$ corresponding to only $3\%$ bromine doping.
Using neutron scattering, we reveal a change of the ground-state from spiral
order in FeCl$_3$ to A-type antiferromagnetic order in FeBr$_3$. Using
first-principles calculations, we show that a delicate balance between nearest
and next-nearest neighbor interactions is responsible for such a transition.
These results support the proximity of FeCl$_3$ to a spiral spin liquid state,
in which competing interactions and nearly degenerate magnetic $k$-vectors may
cause large changes in response to small perturbations.
