In this paper, we examine whether LLMs can generate context-appropriate word order in Russian. Using a new corpus of movie scripts in Russian, with a particular focus on dialogues, we investigate how various semantic, morphosyntactic, and discourse features influence word order choice. We show that traditional machine learning can use these features to model different word order fairly well. We also examine whether LLM dialogue partners can generate context-appropriate word order in Russian. With both zero- and few-shot prompting, LLMs fail to generate word orders beyond the default subject-verb-object. Instead, in order to generate context-appropriate word orders, LLMs need to be fine-tuned or given explicit word order suggestions from a traditional machine learning method.