We extract the e+e-→π+π- cross section in the energy range between 600 and 900 MeV, exploiting the method of initial state radiation. A data set with an integrated luminosity of 2.93 fb-1 taken at a center-of-mass energy of 3.773 GeV with the BESIII detector at the BEPCII collider is used. The cross section is measured with a systematic uncertainty of 0.9%. We extract the pion form factor |Fπ|2 as well as the contribution of the measured cross section to the leading-order hadronic vacuum polarization contribution to (g-2)μ. We find this value to be aμππ,LO(600-900MeV)=(368.2±2.5stat±3.3sys)10-10, which is between the corresponding values using the BaBar or KLOE data.