The BERT family of neural language models have become highly popular due to their ability to provide sequences of text with rich context-sensitive token encodings which are able to generalise well to many NLP tasks. We introduce gaBERT, a monolingual BERT model for the Irish language. We compare our gaBERT model to multilingual BERT and the monolingual Irish WikiBERT, and we show that gaBERT provides better representations for a downstream parsing task. We also show how different filtering criteria, vocabulary size and the choice of subword tokenisation model affect downstream performance. We compare the results of fine-tuning a gaBERT model with an mBERT model for the task of identifying verbal multiword expressions, and show that the fine-tuned gaBERT model also performs better at this task. We release gaBERT and related code to the community.