Roddick blasted nine aces and never lost his serve but still needed more than two hours to beat the 14th-seeded Argentine.
"The difference was his serve," said Chela. "I played a good match but it's difficult when he is serving so well.
"I couldn't do anything."
Roddick, 22, the Washington champion in 2001, rarely lost more than one point on his serve.
"I felt I was controlling the match with my serve," said Roddick. "I thought I was getting the better of him most of the night.
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Roddick, however, broke Chela in the third game of the final set to take a 2-1
"I felt I was on the verge of playing well and then I'd throw in some errors," said Roddick. "But I'm playing better. I'm on the verge of finding some good stuff."
Chela, 24, reached the semi-finals in Los Angeles last week before losing to eventual winner Andre Agassi.
Roddick will face hard-serving Croatian Ivo Karlovic in the quarter-finals on Friday after the 6-foot-10 Karlovic blasted 14 aces to defeat Britain's Greg Rusedski 7-6, 6-2.
In other matches, France's Arnaud Clement survived a slow start and a 16-ace performance by Gilles Muller of Luxembourg to record a 4-6, 6-3, 6-4 victory.
"He is a good player, and I had to play my best tennis to beat him," Clement said. "For me playing this well is raising my confidence for the U.S. Open."
Thailand's Paradorn Srichaphan, a finalist in Washington in 2002, defeated South Africa's Wesley Moodie 6-3, 7-6, easily winning the tiebreaker 7-1.