While misinformation and disinformation have been thriving in social media for years, with the emergence of the COVID-19 pandemic, the political and the health misinformation merged, thus elevating the problem to a whole new level and giving rise to the first global infodemic. The fight against this infodemic has many aspects, with fact-checking and debunking false and misleading claims being among the most important ones. Unfortunately, manual fact-checking is time-consuming and automatic fact-checking is resource-intense, which means that we need to pre-filter the input social media posts and to throw out those that do not appear to be check-worthy. With this in mind, here we propose a model for detecting check-worthy tweets about COVID-19, which combines deep contextualized text representations with modeling the social context of the tweet. We further describe a number of additional experiments and comparisons, which we believe should be useful for future research as they provide some indication about what techniques are effective for the task. Our official submission to the English version of CLEF-2020 CheckThat! Task 1, system Team_Alex, was ranked second with a MAP score of 0.8034, which is almost tied with the wining system, lagging behind by just 0.003 MAP points absolute.