Recent observations of the Magellanic Stream can be used to set limits on a possible hot halo surrounding the Galaxy. The observations are described in detail elsewhere (Mirabel, Cohen & Davies, submitted to Mon. Not. R. astr. Soc.). Briefly, the neutral hydrogen in the northern end of the Magellanic Stream is concentrated in narrow filaments which contain small elongated clouds of typical size 0°.4 × 0°.6. These clouds have a large velocity halfpower width (25 km s−1 and are gravitationally unstable, unless there is a massive low luminosity stellar component. If we consider only the observed gas the expansion age of a typical cloud is 6 × 105 D years, where D is the distance in kpc from the Sun, and this falls at least a factor of ten short of the age of the Stream predicted by current models. This strongly suggests that some containment mechanism is operating.