Large Language Models have vastly grown in capabilities. One potential application of such AI systems is to support data collection in the social sciences, where perfect experimental control is currently unfeasible and the collection of large, representative datasets is generally expensive. In this paper, we re-replicate 14 studies from the Many Labs 2 replication project (Klein et al., 2018) with OpenAI's text-davinci-003 model, colloquially known as GPT3.5. For the 10 studies that we could analyse, we collected a total of 10,136 responses, each of which was obtained by running GPT3.5 with the corresponding study's survey inputted as text. We find that our GPT3.5-based sample replicates 30% of the original results as well as 30% of the Many Labs 2 results, although there is heterogeneity in both these numbers (as we replicate some original findings that Many Labs 2 did not and vice versa). We also find that unlike the corresponding human subjects, GPT3.5 answered some survey questions with extreme homogeneity$\unicode{x2013}$with zero variation in different runs' responses$\unicode{x2013}$raising concerns that a hypothetical AI-led future may in certain ways be subject to a diminished diversity of thought. Overall, while our results suggest that Large Language Model psychology studies are feasible, their findings should not be assumed to straightforwardly generalise to the human case. Nevertheless, AI-based data collection may eventually become a viable and economically relevant method in the empirical social sciences, making the understanding of its capabilities and applications central.