Are the states forbidden by the constitution to keep a militia?

No, the Constitution does not forbid states from maintaining militias. In fact, the Second Amendment recognizes the right to keep and bear arms in the context of a "well-regulated militia." Additionally, Article I, Section 8, empowers Congress to organize, arm, and discipline the militia while reserving to the states the authority to appoint officers and train the militia according to the discipline prescribed by Congress. Thus, states can and do maintain their own militias, often referred to as the National Guard.