  The TRAPPIST-1 system is the first transiting planet system found orbiting an
ultra-cool dwarf star. At least seven planets similar to Earth in radius and in
mass were previously found to transit this host star. Subsequently, TRAPPIST-1
was observed as part of the K2 mission and, with these new data, we report the
measurement of an 18.77 d orbital period for the outermost planet, TRAPPIST-1h,
which was unconstrained until now. This value matches our theoretical
expectations based on Laplace relations and places TRAPPIST-1h as the seventh
member of a complex chain, with three-body resonances linking every member. We
find that TRAPPIST-1h has a radius of 0.727 Earth radii and an equilibrium
temperature of 173 K. We have also measured the rotational period of the star
at 3.3 d and detected a number of flares consistent with a low-activity,
middle-aged, late M dwarf.
