  We present Arecibo Legacy Fast ALFA (ALFALFA) and follow-up Giant Metrewave
Radio Telescope (GMRT) HI observations of the gas-rich interacting group NGC
3166/9. The sensitive ALFALFA data provide a complete census of HI-bearing
systems in the group while the high-resolution GMRT data elucidate their
origin, enabling one of the first unbiased physical studies of gas-rich dwarf
companions and the subsequent identification of second generation, tidal dwarf
galaxies in a nearby group. The ALFALFA maps reveal an extended HI envelope
around the NGC 3166/9 group core, which we mosaic at higher resolution using
six GMRT pointings spanning ~1 square degree. A thorough search of the GMRT
datacube reveals eight low-mass objects with gas masses ranging from 4x10^7 to
3x10^8 M_sol and total dynamical masses up to 1.4x10^9 M_sol. A comparison of
the HI fluxes measured from the GMRT data to those measured in the ALFALFA data
suggests that a significant fraction (~60%) of the HI is smoothly distributed
on scales greater than an arcminute (~7 kpc at the NGC 3166/9 distance). We
compute stellar masses and star formation rates for the eight low-mass GMRT
detections, using ancillary SDSS and GALEX data, and use these values to
constrain their origin. Most of the detections are likely to be either
pre-existing dwarf irregular galaxies or short-lived, tidally formed knots;
however, one candidate, AGC 208457, is clearly associated with a tidal tail
extending below NGC 3166, exhibits a dynamical to gas mass ratio close to unity
and has a stellar content and star formation rate that are broadly consistent
with both simulated as well as candidate tidal dwarf galaxies from the
literature. Our observations therefore strongly suggest that AGC 208457 is a
tidal dwarf galaxy.
