  Exoplanet surveys have shown that systems with multiple low-mass planets on
compact orbits are common. Except for few cases, however, the masses of these
planets are generally unknown. At the very end of the main sequence, host stars
have the lowest mass and hence offer the largest reflect motion for a given
planet. In that context, we monitored the low-mass (0.13Msun) M dwarf YZ Cet
(GJ 54.1, HIP 5643) intensively and obtained both radial velocities and
stellar-activity indicators derived from both spectroscopy and photometry. We
find strong evidence that it is orbited by at least three planets in compact
orbits (P=1.97, 3.06, 4.66 days), with the inner two near a 2:3 mean-motion
resonance. The minimum masses are comparable to that of Earth
(Msini=0.75+-0.13, 0.98+-0.14, and 1.14+-0.17 Mearth) and also the lowest
masses measured by radial velocity so far. We note the possibility for an even
lower-mass, fourth planet with Msini=0.472+-0.096 Mearth at P=1.04 days. An
n-body dynamical model is used to put further constraints on the system
parameters. At 3.6 parsecs, YZ Cet is the nearest multi-planet system detected
to date.
