We present the first radial velocity measurement of the stellar component o
f the Local Group dwarf galaxy Phoenix, using the FORS1 instrument at the V
LT's Unit Telescope 1 (Antu). From the spectra of 31 red giant branch stars
, we derive a heliocentric optical radial velocity for Phoenix of V. = -52
+/- 6 km s(-1). On the basis of this velocity, and taking into account the
results of a series of semianalytical and numerical simulations, we discuss
the possible association of the H I clouds observed in the Phoenix vicinit
y. We conclude that the characteristics of the H I cloud with heliocentric
velocity -23 km s(-1) are consistent with this gas having been associated w
ith Phoenix in the past and being lost by the galaxy after the last event o
f star formation in the galaxy, about 100 Myr ago. Two possible scenarios a
re discussed : the ejection of the gas by the energy released by the supern
ovae (SNe) produced in that last event of star formation and a ram pressure
stripping scenario. We derive that the kinetic energy necessary to eject t
he gas is E-SNe similar to 2 x 10(51) ergs and that the number of SNe neces
sary to transfer this amount of kinetic energy to the gas cloud is similar
to 20. This is consistent with the number of SNe expected for the last even
t of star formation in Phoenix, according to the star formation history der
ived by Gallart, & Aparicio. The drawback of this scenario is the regular a
ppearance of the Martinez-Delgado, H I cloud and its anisotropic distributi
on with respect to the stellar component. Another possibility is that the H
I gas was stripped as a consequence of ram pressure by the intergalactic m
edium. In our simulations, the structure of the gas remains quite smooth as
it is stripped from Phoenix, keeping a distribution similar to that of the
observed H I cloud. Both in the SNe ejection case and in the ram pressure
sweeping scenario, the distances and relative velocities imply that the H I
cloud is not gravitationally bound to Phoenix, since this would require a
Phoenix total mass about an order of magnitude larger than its total estima
ted mass. Finally, we discuss the possibility that Phoenix may be a bound M
ilky Way satellite. The minimum required mass of the Milky Way for Phoenix
to be bound is M-MW (<450 kpc) <greater than or equal to> 1.2 x 10(12) M.,
which comfortably fits within most current estimates.