An equaliser from the visitors deep into stoppage time robbed Avenue of a winning start to the UniBond Division One campaign at Horsfall Stadium.
Despite the home side being well under par, they had kept Chorley at bay and snuffed out any threat to Gavin Kelly's goal until the third minute of injury time.
Manager Trevor Storton was more disgrunted by his misfiring forwards than the result.
"We didn't play well at all, we were shocking up front. We have let a mediocre side take two points off us," he raged.
"At the back Ian Thompson, who actually got the goal on his debut for us, Neil Bagshaw and Paul Marquis were outstanding.
"But the rest of them didn't get hold of it at all. In truth we didn't deserve three points because we have not had a handful of shots on target and that is just not us.
"That type of performance is not satisfactory for me whatsoever. I have told the players to go home and analyse it and to make sure it doesn't happen again."
The visitors had the most possession early in the match but the only save Kelly had to make was from a long range effort by Paul Fleming.
Avenue took the lead through debutant Thompson in the 30th minute. He took possession just inside the visitors half and ran at the opposition.
He arrived on the edge of the area after skipping past the tackles that were coming in from both sides and neatly lobbed Chorley keeper Simon Marsh.
He will claim his earlier attempt, also from a run through the middle, which went three feet over Marsh's crossbar was merely a range finder.
Centre forward Jason Maxwell had a shot well-saved by Marsh and Marquis headed just wide from a Stephen Ball free kick as Avenue tried in vain to add to their lead before the interval.
Fifteen minutes into the second half Storton sent on Chris Dolby, who had not even trained since returning from a fortnight's holiday, in the hope of adding another dimension.
Minutes later another good chance was lost when Dean Calcutt shot just over the bar from the corner of the area.
Chorley refused to let the game go and pressed forward right until the end. Chris Blakeman fired a shot just wide before the visitors' ex-Guiseley defender Stephen Hook headed wide two minutes from time.
Danny Mills finally brought them level with his cruel but beautifully struck drive which gave Kelly no chance.
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