It actually began yesterday, October 21.
Click here for important 2013 election dates in Texas - this is from votetexas.gov.
Click here for similar information from the Secretary of State's office.
Texas Tribune reports that this election will provide an early indication of the impact of voter ID laws in the state.
Early voting is one of a handful of processes that make it easier for people to vote - Tuesday's can be difficult for working people. The NCSL provides a look at the range of methods used by different states. In addition to early voting, there's absentee voting - either with or without an excuse - and all mail voting.
Click here for detail and the map - suffice to say that the political culture in some states - in addition to the political interests in different states - lead to drives to enhance or restrict access to the polls. Texas historically has tended to restrict access, which leads to the suspicion by some that the intent of voter ID laws is to impact the tendency of certain groups to turn out.