Spontaneous long-range nuclear antiferromagnetic order in the spin-1/2 system of silver nuclei was observed by neutron diffraction on a single crystal of Ag-109. A structure with the ordering vector k = (2 pi/a) (0,0,1) developed when the antiferromagnetic state was entered by adiabatic demagnetization along the  axis. No domains of the other two symmetry-equivalent k vectors, (2 pi/a) (0,1,0) and (2 pi/a) (1,0,0), formed during warmup in zero field. Nuclear susceptibility and entropy were found by neutron transmission. In B = 0, the critical entropy of ordering was S-c = (0.54 +/- 0.03)R ln2.