Says the University of Texas library:

 

T. B. Baker, head of the Baker Hotel Company, built the hotel in 1925. Opening night, October 25, 1925, was marked by a Gala dinner dance. According to a Dallas Morning News report, the keys to the building were officially thrownaway at 6:00 Saturday morning, "thus will be symbolized the fact that the portals of the building from hence forward are never to be closed day or right." The opening was also the 30th anniversary of the opening of the old Oriental which has been torn down and the Baker built on the same site.

The Baker was the home of WFAA radio, the Peacock Terrace, Crystal Ballroom, and the place to play on Texas-OU weekends. Its ballrooms were used for debutantes, movie stars, and society members. The Peacock Terrace Ballroom opened in 1925, and the big name swing bands of the 20s and 30s played for Dallasites. The Idlewild Ball for Debutantes was held annually in the Crystal Ballroom. The Petroleum Club met at the Baker. The Mural Room was the main luncheon site for many. The brownstone building catered to Its patrons with style and luxury for 54 years.

It was demolished in 1980. A photo taken right before the implosion can be found here; seems thinner. A great shot of the street from the 60s: here.