Magnetism in the orthorhombic metal CaFe(4)As(3) was examined through neutron diffraction for powder and single crystalline samples. Incommensurate [q(m) ≈ (0.37-0.39) × b*] and predominantly longitudinally (|| b) modulated order develops through a 2nd order phase transition at TN = 89.63(6) K with a 3D Heisenberg-like critical exponent β = 0.365(6). A 1st order transition at T2 = 25.6(9) K is associated with the development of a transverse component, locking q(m) to 0.375(2)b*, and increasing the moments from 2.1(1) to 2.2(3) μ B for Fe2+ and from 1.3(3) to 2.4(4) μB for Fe+. The ab initio Fermi surface is consistent with a nesting instability in cross-linked FeAs strips.