We test whether NLP datasets created with Large Language Models (LLMs) contain annotation artifacts and social biases like NLP datasets elicited from crowd-source workers. We recreate a portion of the Stanford Natural Language Inference corpus using GPT-4, Llama-2 70b for Chat, and Mistral 7b Instruct. We train hypothesis-only classifiers to determine whether LLM-elicited NLI datasets contain annotation artifacts. Next, we use point-wise mutual information to identify the words in each dataset that are associated with gender, race, and age-related terms. On our LLM-generated NLI datasets, fine-tuned BERT hypothesis-only classifiers achieve between 86-96% accuracy. Our analyses further characterize the annotation artifacts and stereotypical biases in LLM-generated datasets.