An alcoholic trying to get sober at a notorious Queens rehab says a director there arranged a job for him — delivering booze and sex toys to a gay chubby-chaser convention.

The man said Carmen Rivera, a manager of the beleaguered J-CAP non-profit, asked him and another patient if they wanted an off-the-books job last summer moving boxes.

He said he thought the gig would be at someone’s home, but instead he was asked to haul cartons from a Queens storage unit to the Hotel Pennsylvania in Manhattan.

The goods were going to Convergence NYC which advertises itself as “The largest annual event for gay chubby men (chubs) and their admirers (chasers).”

While moving one box, he said, “a whole bunch of fake male organs” fell out.

But what was really troubling, he said, was that he and his fellow addict were asked to ferry vodka, whiskey and beer and there was so much of it, they had to hide it in suitcases to smuggle it into the event.

“I was under heavy, heavy temptation,” he said, noting he resisted the urge to drink and is still sober.

The off-campus job was apparently sanctioned by Diane Gonzalez, the CEO of J-CAP, because he was working for a man who identified himself as her brother, Ralph Gonzalez.

Meanwhile, taxpayers were paying for his rehab.

A lawyer for J-CAP’s administrators maintained that “any boxes moved were sealed.”

This is not the first time rehab clients have been given inappropriate jobs. The Post reported in 2014 that program manager Murray Kaplan had clients do housekeeping at his Manhattan and Hamptons homes. One man said he got $20 and a pack of cigarettes for the yard work. Kaplan denied the allegations.

J-CAP is under probe by the state Attorney General and the state Office of Alcoholism and Substance Abuse Services. The program’s management was taken over by another non-profit as of Thursday, according to an OASAS spokesman.