Plastic water glass is sticky after it was put in the dishwasher,

I've a favorite plastic water glass that's always been hand washed. It was accidentally put in the dishwasher, now it's sticky on the outside only. How can the stickiness be removed? It also has a chemical taste now. I'd like to keep the glass.

One common problem with old rubber/plastic items becoming sticky due to surface breakdown with age is often solved by cleaning with ammonia, specifically. If that fails, try rubbing (isopropyl) alcohol.

Wash and rinse throughly in your normal manner afterwards, of course.

It's plausible but not certain that the dishwasher detergent and temperature has accelerated oxidation of the plastic surface in a manner similar to aging, so the same solutions may work.