West Ham striker Teddy Sheringham was denied a winner on his 40th birthday, thanks to an instinctive save by Charlton keeper Thomas Myhre.
There was little to separate West Ham and Charlton at Upton Park
Sheringham had a late chance to snatch a win but his far-post prod from point-blank range was saved by the outstretched arm of Myhre.
West Ham were frustrated for the most part but also had a Bobby Zamora header cleared off the line.
Charlton put in a determined display as both sides had to settle for a point.
West Ham had wasted little time early on in creating a chance, with Yossi Benayoun's long throw being flicked on at the near post by Anton Ferdinand and Ashton shooting high over the bar.
The Hammers are at their best going forward and they took the initiative in the attacking department straight from the kick-off as Marlon Harewood was the next player to go close.
The powerhouse forward expertly controlled a long ball before having a 25-yard shot that spun wide after taking a deflection off defender Chris Perry.
But Charlton slowly nullified the threat of the home side as they held the Hammers at arm's length, while trying to catch them on the counter-attack - through the pace of strikers Darren and Marcus Bent.
West Ham were wise to the danger and both defences took charge of the game as chances were at a premium.
Ferdinand and Harewood each went close with well-struck shots before Darren Bent sent a low, curling strike wide at the other end.
But Sheringham received the biggest cheer of a low-key first half when he began to warm up on the touchline and the veteran striker was duly introduced after the break.
The move did little to unlock a cagey game, although Benayoun did stab a shot wide after a neat one-two with Harewood put him through on goal.
Hammers defender James Collins sent a 30-yard strike just too high as some urgency was injected into the game, with Darren Bent quickly forcing Shaka Hislop into a smart save.
Benayoun swivelled and shot just wide and Zamora had a header cleared off the line by Radostin Kishishev as West Ham pressed for a winner.
Sheringham had a late chance - only for the outstretched arm from Myhre to deny him a birthday goal.
West Ham: Hislop, Ferdinand, Collins, Gabbidon, Konchesky, Benayoun, Mullins, Reo-Coker (Zamora 75), Etherington, Ashton (Sheringham 45), Harewood (Katan 86).
Subs Not Used: Walker, Scaloni.
Charlton: Myhre, Young (Spector 62), Perry, Hreidarsson, Powell, Rommedahl (Thomas 70), Kishishev, Holland, Hughes, Marcus Bent (Bothroyd 86), Darren Bent.
Subs Not Used: Andersen, Euell.
Ref: R Styles (Hampshire).