Amid the incense, cheap art and herbal remedies for sale in Union Square in Manhattan on Monday, a very different kind of product was changing hands: bitcoins.

Just feet from the park’s statue of George Washington, a crowd of young men gathered on Monday afternoon to buy and sell the digital, crypto-currency.

The men – and there were only men – were brought together by an online posting from Josh Rossi, 31, a bitcoin aficionado who works in technology at the World Trade Financial Group.

One of the trademarks of bitcoins since they were created by anonymous programmers in 2009 has been that they have no physical form, and can be exchanged completely electronically, making human interactions unnecessary.

But the online venues for buying and selling bitcoins have become too expensive and time consuming, Mr. Rossi said. So he proposed what he called Project Buttonwood, a reference to the where the New York Stock Exchange had its beginning in 1792.

“If I want to buy a hamburger, I want to be able to sell my bitcoins and get my money immediately so I can buy that hamburger,” said Mr. Rossi, who wore jeans and loafers for the occasion, and smoked a cigarette while watching the proceedings.

The legality of bitcoin has been questioned by some regulators, and investors have looked on in horror in recent weeks as the price of a single bitcoin has bounced around more sharply than the most speculative stock. Mr. Rossi’s posting about the event on Reddit was sniped at by one commentator who said “you might get busted by the Feds” and another who predicted “the first bitcoin ‘gang’ fight.”

In the end, such dire predictions did not pan out. After a slow start at 4 p.m., just as trading on the New York Stock Exchange shut down for the day, the crowd grew to about 20 people. There were a few polite arguments about how the process should work, and then people began calling out prices at which they were willing to buy and sell bitcoins. Many of the young men alternated between conversation and watching the nearby skateboarders and break dancers.

The first transaction came when Mr. Rossi pulled out a $20 bill in order to buy a part of a bitcoin, at a rate of $120 for a single bitcoin. The seller was Owen Gunden, a 30-year old programmer. In order to transfer the online currency, Mr. Rossi used his smartphone to take a picture of the graphic code on Mr. Gunden’s phone, which provided access to his bitcoin account. The crowd around the men clapped.

“This is markets becoming more efficient,” Mr. Rossi said with a smile.

Nearby, Kirill Gourov, a 21-year old college student, said he was looking to buy a bitcoin for $125 and was serving as a broker for a friend who was text messaging him, and who wanted to sell his bitcoin for $112.

The gap between the bid and offer in Union Square was significantly larger than it was at the same time on the biggest online exchange, Mt. Gox, where the going price was around $114. But before long, a few more buyers and sellers met. Gabe Sukenik, the 24-year old founder of a bitcoin start-up, Coinapult, pulled out a wad of $20 bills and counted out enough cash to buy two bitcoins from a young man who identified himself as a Wall Street trader.

“I’ll flip a coin for a hundred bucks if you want,” said the trader. “That’s my risk tolerance.”

As the afternoon went on, a man who gave his name as Jerry, took out a notebook and began recording the trickle of trades. He jokingly said he would serve as the exchange’s clerk if someone bought him a Coke.

“We’re here enjoying the sunshine, enjoying the ladies, and trying to move the bitcoin community along,” Jerry said.

Mr. Rossi said he planned to be back in the same place next Monday.