The purpose of the present study is to examine how first-year Thai undergraduate students who learn English as a Foreign Language (EFL) use referential forms in telling a coherent story in English. Participants were at intermediate level of English proficiency. The study aims to discover the referential strategies the Thai EFL learners adopt to achieve discourse cohesion and find out whether or not the referential forms used correspond to the discourse context and Du Bois' (1987) preferred Argument Structure (PAS). Using Mayers' wordless picture book "Frog, Where Are You?" (1969) as prompts, the participants were asked to tell the story in English. The narratives were tape-recorded and later analyzed. The data were coded on three criteria: (1) referential forms (Lexical, Pronominal, Null); (2) discourse contxts (New, Old, Active, Previous Subject); and (3) grammatical functions (S: intransitive subject, A: transitive subject, A: transitive subject, O: transitive object). The result of the study demonstrates that Thai EFL learners use a full noun phrase when referring to a character first introduced in the story and one already mentioned when a pronoun is used if the referent is the subject of the previous clause. This finding corresponds to the PAS. Narrators avoid more than one lexical argument per clause, more than one new argument per clause, and new A's. However, the Non-Lexical A constraint (avoid lexical A's) is violated, suggesting that, the Thai participants are limited in their linguistic ability to achieve complete discourse cohesion in English storytelling, despite using almost the same referential strategies as native English speakers. Limiting factors observed include language transfer, over-explicitness, and topic discontinuity.