Here is a question about this article: From earliest days, Virginia, and Richmond in particular, have welcomed live theatrical performances. From Lewis Hallam's early productions of Shakespeare in Williamsburg, the focus shifted to Richmond's antebellum prominence as a main colonial and early 19th century performance venue for such celebrated American and English actors as William Macready, Edwin Forrest, and the Booth family. In the 20th century, Richmonders' love of theater continued with many amateur troupes and regular touring professional productions. In the 1960s a small renaissance or golden age accompanied the growth of professional dinner theaters and the fostering of theater by the Virginia Museum, reaching a peak in the 1970s with the establishment of a resident Equity company at the Virginia Museum Theater (now the Leslie Cheek) and the birth of Theatre IV, a company that continues to this day.
What is the answer to this question: During what decade did the Virginia Museum most significantly work to promote theater in Richmond?
1970s
The context mentions a "small renaissance or golden age" in the 1960s, which reached its peak during the 1970s.
It also states that Theater IV was born at this time. The theater continues to operate today and is one of Richmond's most notable theaters. 
Based on these facts, we can infer that it must be the decade where Virginia Museum worked hardest to promote theater in Richmond: The 1970s.