Researchers in different social science disciplines have successfully used Facebook to recruit subjects for their studies. However, such convenience samples are not generally representative of the population. We developed and validated a new quota sampling method to recruit respondents using Facebook advertisements. Additionally, we published an R package to semi-automate this quota sampling process using the Facebook Marketing API. To test the method, we used Facebook advertisements to quota sample 2432 US respondents for a survey on climate change public opinion. We conducted a contemporaneous nationally representative survey asking identical questions using a high-quality online survey panel whose respondents were recruited using probability sampling. Many results from the Facebook-sampled survey are similar to those from the online panel survey; furthermore, results from the Facebook-sampled survey approximate results from the American Community Survey (ACS) for a set of validation questions. These findings suggest that using Facebook to recruit respondents is a viable option for survey researchers wishing to approximate population-level public opinion.