Is men's 50 m pistol still an olympic event? Jin Jong-oh has won that event 3 times in a row, so if it still is an olympic events and he hasn't retired yet, then he might have a chance.
He also won silver in 2004, so he was very close already.
Dario Cologna also is an interesting case. He won the 15 km race 3 times in a row, 2010 and 2018 in freestyle and 2014 in classical style. He could win a 4th gold in 2022.
Saori Yoshida was also pretty close, she won gold in women's -55 kg wrestling in 2004, 2008 and 2012, but "only" silver in the -53 kg category in 2016.
Shaun White could also win his 4th gold in the halfpipe in 2022, but i don't know if he even plans to compete?
Mijain Lopez won gold in 2008 (-120 kg), 2012 (-120 kg) and 2016 (-130 kg), so he could also win his 4th gold in 2020 (don't know if he is still active?).