Entity Resolution (ER) is the problem of semi-automatically determining when two entities refer to the same underlying entity, with applications ranging from healthcare to e-commerce. Traditional ER solutions required considerable manual expertise, including domain-specific feature engineering, as well as identification and curation of training data. Recently released large language models (LLMs) provide an opportunity to make ER more seamless and domain-independent. However, it is also well known that LLMs can pose risks, and that the quality of their outputs can depend on how prompts are engineered. Unfortunately, a systematic experimental study on the effects of different prompting methods for addressing unsupervised ER, using LLMs like ChatGPT, has been lacking thus far. This paper aims to address this gap by conducting such a study. We consider some relatively simple and cost-efficient ER prompt engineering methods and apply them to ER on two real-world datasets widely used in the community. We use an extensive set of experimental results to show that an LLM like GPT3.5 is viable for high-performing unsupervised ER, and interestingly, that more complicated and detailed (and hence, expensive) prompting methods do not necessarily outperform simpler approaches. We provide brief discussions on qualitative and error analysis, including a study of the inter-consistency of different prompting methods to determine whether they yield stable outputs. Finally, we consider some limitations of LLMs when applied to ER.