Unfortunately, it will take at least two days to drive from Chicago to Houston. The best and fastest route is via I-57 South, I-40 West, I-30 West, US-59 South, and I-69 South—but even that route will take you 16 hours and 30 minutes to complete during low-traffic periods.
If you want to get from Chicago to Houston in one day, your best bet is to fly. Round trip tickets are between $200 and $600 depending on the travel dates and airline you choose. Compare this to a $350 gas bill plus a hotel room and you might even save some money by flying!