  We present the first results from AMUSE-Field, a Chandra survey designed to
characterize the occurrence and intensity of low-level accretion onto
supermassive black holes (SMBHs) at the center of local early-type field
galaxies. This is accomplished by means of a Large Program targeting a
distance-limited (<30 Mpc) sample of 103 early types spanning a wide range in
stellar masses. We acquired new ACIS-S observations for 61 objects down to a
limiting (0.3-10 keV) luminosity of 2.5x10^38 erg/s, and we include an
additional 42 objects with archival (typically deeper) coverage. A nuclear
X-ray source is detected in 52 out of the 103 galaxies. After accounting for
potential contamination from low-mass X-ray binaries, we estimate that the
fraction of accreting SMBHs within the sample is 45+/-7 percent, which sets a
firm lower limit on the occupation fraction within the field. The measured
nuclear X-ray luminosities are invariably highly sub-Eddington, with
-8<log(L_X/L_Edd)<-4. As also found in a companion survey targeting Virgo early
types, the active fraction increases with increasing host galaxy stellar mass,
reflective of "Eddington incompleteness" within the lower-mass objects. For the
Field sample, the average nuclear X-ray luminosity scales with the host stellar
mass as M_star^(0.71+/-0.10), with an intrinsic scatter of 0.73+/-0.09 dex. A
majority of the AMUSE-Field galaxies (78%) inhabits groups, enabling us to
investigate the influence of group richness upon nuclear activity. We see no
evidence for a positive correlation between nuclear X-ray luminosity,
normalized to host properties, and galaxy density. Rather, while the scatter is
substantial, it appears that the Eddington-scaled X-ray luminosity of group
members may be slightly lower than for isolated galaxies, and that this trend
continues to cluster early-types.
