Magnetic trapping of bromine atoms at temperatures in the millikelvin regime is demonstrated for the first time. The atoms are produced by photodissociation of Br2 molecules in a molecular beam. The lab-frame velocity of Br atoms is controlled by the wavelength and polarization of the photodissociation laser. Careful selection of the wavelength results in one of the pair of atoms having sufficient velocity to exactly cancel that of the parent molecule, and it remains stationary in the lab frame. A trap is formed at the null point between two opposing neodymium permanent magnets. Dissociation of molecules at the field minimum results in the slowest fraction of photofragments remaining trapped. After the ballistic escape of the fastest atoms, the trapped slow atoms are lost only by elastic collisions with the chamber background gas. The measured loss rate is consistent with estimates of the total cross section for only those collisions transferring sufficient kinetic energy to overcome the trapping potential.