Chelsea new jersey fa cup
You're referring to the Chelsea FC team based in New Jersey, USA!
Chelsea FC New Jersey is a semi-professional soccer team that plays in the National Premier Soccer League (NPSL), which is the fourth tier of the American soccer pyramid. The team was founded in 2013 and is affiliated with the English Premier League club Chelsea FC.
As for the FA Cup, it's a domestic cup competition in England, and Chelsea FC New Jersey is not eligible to participate in it since they are a US-based team. The FA Cup is open to clubs playing in the top 10 tiers of English football, and Chelsea FC New Jersey does not meet those criteria.
However, the team does compete in the US Open Cup, which is the national cup competition in the United States. They have participated in the tournament several times, including in 2014, 2015, and 2016.
I hope that answers your question!