This paper introduces definitions of Thai elementary discourse units (T-EDUs), grammar rules for T-EDU segmentation, and two versions of chart parsing for T-EDU detection; one with longest matching and the other with maximum matching. Four different environments are investigated; close test with a pre-chunked text, close test with a running text, open test with a pre-chunked text, and open test with a running text. As our test-bed, 1,530 T-EDUs extracted from the NE- and POS-tagged Thai-NEST corpus are used to construct a set of context free grammar (CFG) rules and then the rules are applied to segment T-EDUs from a text. With consideratioh of all generated edges (T-EDUs) without syntactic constraints, longest matching (LM) or maximum matching (MM) are developed to select possible T-EDUs. The result shows that on the pre-chunked text, the precisions can be improved from 28.64% to 92.53% and 92.70%, respectively with minor sacrifice of 7-8% recall, dropping to 93.01% and 92.09%, respectively. ©2013 International Information Institute.