We present the first radial velocity measurement of the stellar component of the Local Group dwarf galaxy Phoenix , using FORS1 at the VLT UT1 ( ANTU ) telescope . From the spectra of 31 RGB stars , we derive an heliocentric optical radial velocity of Phoenix V _ { \odot } = -52 \pm 6 { km~ { } s } ^ { -1 } . On the basis of this velocity , and taking into account the results of a series of semi-analytical and numerical simulations , we discuss the possible association of the HI clouds observed in the Phoenix vicinity . We conclude that the characteristics of the HI cloud with heliocentric velocity –23 { km~ { } s } ^ { -1 } are consistent with this gas having been associated with Phoenix in the past , and lost by the galaxy after the last event of star formation in the galaxy , about 100 Myr ago . Two possible scenarios are discussed : the ejection of the gas by the energy released by the SNe produced in that last event of star formation , and a ram-pressure stripping scenario . We derive that the kinetic energy necessary to eject the gas is E _ { SNe } \sim 2 \times 10 ^ { 51 } erg , and that the number of SNe necessary to transfer this amount of kinetic energy to the gas cloud is \sim 20 . This is consistent with the number of SNe expected for the last event of star formation in Phoenix , according to the star formation history derived by Martínez-Delgado et al . ( 1999 ) . The drawback of this scenario is the regular appearance of the HI cloud and its anisotropic distribution with respect to the stellar component . Another possibility is that the HI gas was stripped as a consequence of ram–pressure by the intergalactic medium . 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 HI cloud . Both in the SNe ejection case and in the ram-pressure sweeping scenario , the distances and relative velocities imply that the HI cloud is not gravitationally bound to Phoenix , since this would require a Phoenix total mass about an order of magnitude larger than its total estimated mass . Finally , we discuss the possibility that Phoenix may be a bound Milky Way satellite . The minimum required mass of the Milky Way for Phoenix to be bound is M _ { MW } ( < 450 { kpc } ) \geq 1.2 \times 10 ^ { 12 } M _ { \odot } which comfortably fits within most current estimates .