How is Obama a chief of state?

The proper term is "Head of State".

The Head of State of a country formally represents that country, and in many ways, can be said to be the country. In many nations, the Head of State is also the Chief Executive - that is, the Head of State is also the person in charge of the Executive branch of government. This is the case in most Representative Democracies, though there do exist a number where the Head of State is merely a ceremonial post, and has no real power. Constitutional Monarchies, however, draw a sharp line between the Chief Executive and the Head of State, with the monarch typically holding the latter position, and the Prime Minister holding the former.

The United State's government form is a Presidential system. The design the system is such that the President is considered both Head of State and Chief Executive. Thus, whomever is elected President is Head of State.