The result came in spite of a gearbox issue in the earlier practice, which cost the team almost all the running in the morning.
The Indian driver started on intermediate tyres following a heavy rainstorm between practice and qualifying, completing four laps with a best time of 1:53.957.
He then moved to the slick tyre for his flying laps. He completed six further laps on the dry tyres, improving to a 1:46.758 to put the HPD ARX 03a into seventh overall.
Chandhok said a quicker time was on the cards, but traffic put paid to further improvement.
"Today we were even closer to the front of the field and there was only a hair's breadth between ourselves, Strakka and Rebellion. This is a big step forward over the previous races where we have been a lot further back," said Chandhok.
"We could have gone even faster