The ternary iron chalcogenides KFeS2 and RbFeSe2 consisting of chains of edge sharing FeX4 (X = S, Se) tetrahedra have been investigated by means of magnetic susceptibility, specific heat, Mössbauer, and electron spin resonance measurements. The single crystals exhibit collinear antiferromagnetic (AFM) order with strongly reduced moments below TN = 252 K and 248 K, respectively. For both compounds the small anomaly in the specific heat and the corresponding low value of entropy at TN indicate a significant spin reduction and the existence of AFM fluctuations even far above TN. Mössbauer parameters determined in the entire temperature range indicate that iron in RbFeSe2 is in ferric (trivalent) state having strong covalent bonding to selenium ligands. The measured hyperfine field of 216 kOe at 4.2 K is significantly reduced as compared to that in high-spin ferric compounds corroborating the strong spin reduction of Fe3+. The linear increase of the high-temperature susceptibility data of KFeS2 and RbFeSe2 suggest a one-dimensional metallic character along the chains.