  The TeV binary system LS I +61$^\circ$ 303 is known for its regular,
non-thermal emission pattern which traces the orbital period of the compact
object in its 26.5 day orbit around its B0 Ve star companion. The system
typically presents elevated TeV emission around apastron passage with flux
levels between 5% and 15% of the steady flux from the Crab Nebula (> 300 GeV).
In this article, VERITAS observations of LS I +61$^\circ$ 303 taken in late
2014 are presented, during which bright TeV flares around apastron at flux
levels peaking above 30% of the Crab Nebula flux were detected. This is the
brightest such activity from this source ever seen in the TeV regime. The
strong outbursts have rise and fall times of less than a day. The short
timescale of the flares, in conjunction with the observation of 10 TeV photons
from LS I +61$^\circ$ 303 during the flares, provides constraints on the
properties of the accelerator in the source.
