This is, of course, the chapel founded by Father Gommar DePauw of the "Catholic Traditionalist Movement".  Does anyone know which bishop serves that chapel now (confirmation, oils, etc.), where their priests come from, and are they sedevacantist?

Just sheer curiosity.  I do know (someone correct me if I'm wrong) that Fr DePauw was incardinated under some bishop in Italy, or a similar situation.  I visited that chapel over 30 years ago, just the one time.

The CTM website makes clear they are not sedevacantist, but it is old, archival looking. Fr de Pauw took pains to be have canonical rights to offer the Mass of Ages, no state of emergency, no supplied jurisdiction. I thought it was now SSPX but that would not a close match for what Fr de Pauw hoped, but secular and regular priests with traditional orders are either very old, or rare SSPX-FSSP defection, and are themselves no younger.

The Reagan Presidential Library has a folder of material on Fr de Pauw.

The whole CTM phenomenon has this "frozen in time" look and feel to it, as though Fr DePauw is still around (even though, sadly, he is not), and as far as I can tell, they say nothing about what bishop provides these various functions for them, nor where their new priests come from.  (The latter would be easy, there would be any number of diocesan priests, sympathetic to the traditionalist movement, who might either be retired and willing to relocate to Long Island, or who might leave the Novus Ordo out of unease over that environment.)  I'm sure people who actually go to that chapel, know which bishop comes to do confirmations. 

Interesting.  Does this chapel still have a priest, or do they still gather to watch old video tapes of Fr. de Pauw’s Masses?  The newer links on the website don’t work, and the entire site looks very dated.  I read the requirements for a replacement priest and wonder if any such person even exists today.  Surely there are priests who agree with the doctrinal statements, but as to the requirements for his consecrating bishop, the closest would probably be the SSPX, but it’s not exact. 

So far as I am aware, they have a priest, but I don't know anything about him.

Just going out on a kind of limb, I have to wonder if the SSPX would discreetly visit that chapel for confirmations, similar to the arrangement that St Athanasius in Virginia had with the SSPX before Fr Ringrose went with the Resistance.