We introduce the Faetar Automatic Speech Recognition Benchmark, a benchmark corpus designed to push the limits of current approaches to low-resource speech recognition. Faetar, a Franco-Provençal variety spoken primarily in Italy, has no standard orthography, has virtually no existing textual or speech resources other than what is included in the benchmark, and is quite different from other forms of Franco-Provençal. The corpus comes from field recordings, most of which are noisy, for which only 5 hrs have matching transcriptions, and for which forced alignment is of variable quality. The corpus contains an additional 20 hrs of unlabelled speech. We report baseline results from state-of-the-art multilingual speech foundation models with a best phone error rate of 30.4%, using a pipeline that continues pre-training on the foundation model using the unlabelled set.