Question

If no presidential candidate wins a majority of electoral votes, who can choose the president.

http://www.usconstitution.net/const.html#A2Sec1

In addition to the above excellent answer please consider the following.

The lack of any candidate receiving a majority if the electoral college leads to what is called a contingent election. Scroll down to the section called "Election in the House and Senate". LWV | Who Will Elect the President?
The Electoral College SystemSection=Home&CONTENTID=2176&TEMPLATE=/CM/ContentDisplay.cfm

A problem soon emerged with what occurred in the election of 1800

Presidential Election of 1800 http://www.multied.com/elections/1800.html.

The above led to the 12th Amendment. This site gives you a copy of the 12th Amendment and also in the annotations explains the reasons for its issuance.

U.S. Constitution: Twelfth Amendment http://caselaw.lp.findlaw.com/data/constitution/amendment12/

Answer 1

a bill has been approved in the house and senate albeit in slightly different versions the bill now goes