We report the results of direct measurement of remanent hysteresis loops on nanochains of BiFeO$_3$ at room temperature under zero and $sim$20 kOe magnetic field. We noticed a suppression of remanent polarization by nearly $sim$40% under the magnetic field. The powder neutron diffraction data reveal significant ion displacements under a magnetic field which seems to be the origin of the suppression of polarization. The isolated nanoparticles, comprising the chains, exhibit evolution of ferroelectric domains under dc electric field and complete 180$^o$ switching in switching-spectroscopy piezoresponse force microscopy. They also exhibit stronger ferromagnetism with nearly an order of magnitude higher saturation magnetization than that of the bulk sample. These results show that the nanoscale BiFeO$_3$ exhibits coexistence of ferroelectric and ferromagnetic order and a strong magnetoelectric multiferroic coupling at room temperature comparable to what some of the type-II multiferroics show at a very low temperature.
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