Some history from Wikipedia:

The State House was designed by Charles Bulfinch as a replacement for the Old State House. The cornerstone was laid by John Hancock, who previously used the location as a cow pasture, and the building was completed on January 11, 1798. However, eighty years after the building's dedication, the original red-brick building was deemed too small and there were proposals to build a new state house in the geographical center of the state. Instead, the State House was expanded. The first was the rear addition which was added in 1831. This addition was later expanded in 1853 to 1856 and again in 1889 to 1895 by Charles Brigham. Between 1914 and 1917, two wings made of Vermont marble were added to the west and east ends of the original building to designs by Richard Clipston Sturgis.

The State House's exterior colors also changed. The entire building was painted white in 1825 and later yellow-gold in 1855. With the addition of the east and west wings, the building was again painted white. In 1928, all of the paint was removed, resulting in the current color scheme of the State House.

Furthermore, the dome itself wasn't always gold. After being clad in copper, it was first painted gray and then light yellow. The dome was repainted gray in 1831. It was not gilded with gold leaf until 1874. However, the dome was painted gray during World War II to prevent enemy ships from using the dome to aim their guns.

The building's exterior underwent a major renovation in 2001 and 2002. During that time, the exterior was covered with a shroud with pictures of three hills, including Beacon Hill, that once stood in the area.