As a regional team, they played home games in Richmond, Hampton, and Roanoke as well as a season with Norfolk.

There was a major contract dispute with the cross-bay San Francisco Warriors of the established National Basketball Association over the rights to star player Rick Barry.

He was a former NBA Rookie of the Year who had led the Warriors to the NBA finals in the same year the Oaks had formed, but due to being angered by management's failure to pay him certain incentive awards he felt he was due, he sat out the 1967–68 season, and the following season he joined the Oaks, leading the franchise to its one and only ABA championship in 1969.

The team colors of green and gold were retained, but the logo was a red, white and blue rendition of the United States Capitol.

Merger talks with the NBA were already underway entering the 1970s, but a major stumbling block was the presence of the Caps in Washington.

The name choice ultimately cost the team any goodwill it might have otherwise earned from Pollin, who viewed it as a brazen attempt to pry away the loyalties of fans in Northern Virginia who otherwise mostly support Washington sports teams, and ensured his enduring opposition to Virginia ever being admitted to the NBA in a merger (to the point where the first merger plan in 1971 sought to exclude the Squires franchise unless they moved to a new location instead).

In spite of the initial controversy surrounding Barry, the Squires finished their inaugural season in Virginia by winning the Eastern Division by 11 games.

Although blessed with a combination of Julius Erving ("Dr. J") and a young George Gervin, the duo only played together late in the season.

ABA commissioner Mike Storen tried to block the sale on the grounds that selling the team's last true star was not in the best interest of the league.

While the trades may have provided enough short-term financing to help keep the Squires in business, the loss of so much talent that had been acquired by the franchise (primarily with fantastic draft choices) angered the fans.

The Squires' final two seasons in the ABA were seen as absolutely forgettable with losses mounting up and long-time popular coach Al Bianchi eventually being fired.

The Squires had nearly shut down for good in February 1976 and nearly forced the ABA to complete their season with only six teams instead, but they had only managed to stay afloat thanks to a sale of advertising banners combined with a $250,000 loan from a local bank.