  We search for the decay B0 -> rho0 rho0 in a data sample of about 227 million
Upsilon(4S)-> BBbar decays collected with the BABAR detector at the PEP-II
asymmetric-energy e+e- collider at SLAC. We find no significant signal and set
an upper limit of 1.1*10^-6 at 90% CL on the branching fraction. As a result,
the uncertainty due to penguin contributions on the CKM unitarity angle alpha
measured in B -> rho rho decays is 11 degrees at 68% CL.
