  Negative mass makes perfect physical sense as long as the dominant energy
condition is satisfied by the corresponding energy-momentum tensor. Heretofore,
only {\it configurations} of negative mass had been found
\cite{Belletete:2013nqa,Mbarek:2014ppa}, the analysis did not address stability
or dynamics. In this paper, we analyze both of these criteria. We demonstrate
the existence of {\it stable}, static, negative mass bubbles in an
asymptotically de Sitter space-time. The bubbles are solutions of the Einstein
equations and correspond to an interior region of space-time containing a
specific mass distribution, separated by a thin wall from the exact, negative
mass Schwarzschild-de Sitter space-time in the exterior. We apply the Israel
junction conditions at the wall. For the case of an interior corresponding
simply to de Sitter space-time with a different cosmological constant from the
outside space-time, separated by a thin wall with energy density that is
independent of the radius, we find static but unstable solutions which satisfy
the dominant energy condition everywhere. The bubbles can collapse through
spherically symmetric configurations to the exact, singular, negative mass
Schwarzschild-de Sitter solution. Interestingly, this provides a
counter-example of the cosmic censorship hypothesis. Alternatively, the
junction conditions can be used to give rise to an interior mass distribution
that depends on the potential for the radius of the wall. We show that for no
choice of the potential, for positive energy density on the wall that is
independent of the radius, can we get a solution that is non-singular at the
origin. However, if we allow the energy density on the wall to depend on the
radius of the bubble, we can find {\it stable}, static, non-singular solutions
of negative mass which everywhere satisfy the dominant energy condition.
