The Clarets were behind after seven minutes when Chris Holroyd slid in to turn in a cross that Brian Jensen failed to collect, but their lead lasted only nine minutes when Jonah struck.
He hit a powerful shot low past former Burnley loan goalkeeper Gavin Ward and although there were chances at both ends of the pitch the score remained at 1-1 up to the interval.
Again the second half was an even affair with Ade Akinbiyi, booked early in the half, coming closest to winning it for the Clarets, but neither side could grab the initiative and it ended without any further addition to the score.
The point won't be enough to lift us any higher than third place in the table and next week we return home, if Accrington can be called home, and a game against Morecambe.
Chester: Ward, Vaughan, Newton, Gregory, Kelly, Sandwith, Walker ( Morrin 75), Owen, McManus, Holroyd, Rutherford. Subs not used: Rule, Williams, Rowlands, Thorpe.
Burnley: Brian Jensen, Dean Stott, Dan Brown, Nik Kudiersky, Thomas Bradley (Ben Hoskin 89), Steve Jones, Adam Kay (Alex-Ray Harvey 73), James O'Connor, Garreth O'Connor, Ade Akinbiyi, Rob Turner (Alex McDonald 73). Subs not used: Jonathan Sergeant, Lewis Craig.