This claim is true. According to many different sources, the East Wing of the White House has started to be demolished by construction vehicles. There are videos going around of the process of the demolition and according to a live stream from ABC News, it is currently underway. The president has stated that the ballroom is planned to be built where the East Wing resides. It is estimated to be 90,000 square feet and is will have a seating capacity of 999 persons.
A live stream from ABC News is currently filming the demolition. This shows that the East wing is being taken down in current time. Video Construction crews begin demolition on the East Wing of the White House | Watch Live News on ABCNL
NBC's Today reported on this project. During this video, it shows segments of the president addressing the status of the project. It also provides information that this project is being privately funded. Crews Begin Tearing Down WH East Wing for Trump Ballroom
AP News provided an article, including many details of this project. The information on the size and seating capacity came from this article. White House starts East Wing demolition for Trump's ballroom | AP News
Each source might have biases based on their political views and their opinion of the current presidential administration. But the evidence of this event seems to be pretty straight to the point, that being that the East Wing of the white house is being torn down to make room for a new ballroom. each source may provide their opinion on the matter and have influences that way.
The video of the demolition, the live stream, and the article from AP news all support the claim. They provide photos and information that align with one another and all support each other.
None seem to undermine the claim.