We have measured the freezing curve of liquid H2SO4/H2O aerosol droplets having average radii of approximately 0.2 μm. We form the aerosol by the reaction of SO3 with H2O and flow it through a temperature-controlled flow tube equipped with reentrant windows, through which we make observations by FTIR extinction spectroscopy. At the freezing point, a microcrystallite of pure ice (H2O(s)) nucleates in the aerosol droplet, and this causes a small change in the spectrum near 3250 cm-1. By recording the temperatures at which the crystallites appear for different acid concentrations, we are able to map out the freezing curve. In the following account, we describe the experimental technique and report the freezing curve for the concentration range up to 35 wt % H2SO4, which corresponds to the first eutectic point on the phase diagram of the bulk material. We find that the aerosol supercools by about 35 K below the temperature at which the corresponding bulk material freezes. Our data show that the overall freezing mechanism is similar to that of the bulk solution:  after nucleation, the crystallite grows with decreasing temperature, causing the remaining acid to become more concentrated due to the removal of H2O until eventually a eutectic mixture forms.