Anecdotal evidence suggests that it is fairly common: https://www.reddit.com/r/COVID19positive/ -- 2 of the 5 top posts from today are from people complaining about experiencing this, and are both full of comments personally relating to it. There is obviously going to be a selection bias here, but it seems like a good starting point for estimating a lower bound if you can't find enough good studies.

This study finds about a third of patients self-report fatigue at 2-3 weeks after a positive coronavirus test. That might be a reasonable generous upper bound for the likelihood of chronic fatigue, though I wouldn't trust telephone studies of self-reported symptoms all that much.

From a Nature news article last week:

One study7 of 143 people with COVID-19 discharged from a hospital in Rome found that 53% had reported fatigue and 43% had shortness of breath an average of 2 months after their symptoms started. A study of patients in China showed that 25% had abnormal lung function after 3 months, and that 16% were still fatigued8.

https://institute.global/policy/long-covid-reviewing-science-and-assessing-risk

From the COVID Symptom Study in the UK (app based questionaire), "10 per cent of those taking part in the survey had symptoms of long Covid for a month, with between 1.5 and 2 per cent still experiencing them after three months", and they claim "long Covid is likely a bigger issue than excess deaths as a result of Covid, which are between 0.5 per cent and 1 per cent".

App-based survey, so not necessarily representative of population. Not clear how severe the 3 month cases are, though they state "The most common reported symptom has been described by doctors as “profound fatigue”". Article also summarizes other related studies.