Diffuse X-ray emission originating inside LMC 4, the largest supergian
t shell in the LMC, has been detected in a pointed ROSAT PSPC observat
ion. This is the first detection of a well-defined supergiant shell in
X-rays and the first time that, a background-free spectrum of hot gas
originating from inside a supergiant shell has been derived. The spec
trum can be attributed to emission from a thin thermal plasma of a tem
perature of 2.4 x 10(6) K. We have derived surface brightness, electro
n density, and pressure of the hot gas and investigated the evolutiona
ry state of the supergiant shell. We find LMC 4 to be aged while the h
ot plasma inside still has significant overpressure compared to the su
rrounding gas. Implications of our results for the LMC and supergiant
shells in other galaxies are discussed.