We report on Australia Telescope Compact Array observations in the directio
n of the young high magnetic-held pulsar J1119 - 6127. In the resulting ima
ges we identify a nonthermal radio shell of diameter 15', which we classify
as a previously uncataloged young supernova remnant, G292.2-0.5. This supe
rnova remnant is positionally coincident with PSR J1119-6127, and we conclu
de that the two objects are physically associated. No radio emission is det
ected from any pulsar wind nebula (PWN) associated with the pulsar; our obs
erved upper limits are consistent with the expectation that high magnetic-f
ield pulsars produce radio nebulae that fade rapidly. This system suggests
a possible explanation for the lack of an associated radio pulsar and/or PW
N in many supernova remnants.