LA Galaxy beat Los Angeles FC 2-0 in the US Open Cup, and after Puig scored the second, he whipped off his number six shirt and held it up to the crowd.
The celebration was a mirror of his former Barca teammate Lionel Messi, who iconically held his shirt up to the Bernabeu crowd during a match against Real Madrid in 2017.
But Juventus and Italy legend Chiellini wasn't at all happy, shouting 'payaso!' or 'clown' at the Spaniard who was in the midst of a post-match interview.
Puig undoubtedly had reason to be overjoyed, with his goal an absolutely stunning dribble to make amends for an earlier penalty miss.
During his incredible run from midfield, he left defenders on the floor to cap the victory and seal a spot in the quarter-finals of the cup.
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Chiellini, who didn't play, clearly thought it was an over-celebration though, considering the fact that in the league his LAFC top the Eastern Conference with 25 points from 12 games, while Puig's LA Galaxy are bottom with nine points from 13 games.
Chiellini moved to the US in 2022 after a trophy-filled career in Italy, and quickly added to his honours as Gareth Bale helped LAFC win their first MLS Cup later that year.
It was an expected move for the now 38-year-old defender, but the same can't be said for Puig who surprisingly left Barca at the age of 22.
With the club in the midst of financial difficulties, Puig left at the expiration of his contract in Spain, but Barca have the option to re-sign him and will receive 50 per cent of any future sale.
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The transfer was still a huge surprise, though, with Puig one of the most exciting prospects out of Barcelona's academy that also produced his former teammate Messi.