Maybe, MAYBE there's a chance.
For example, if somebody gives themselves to help another person, without any reward or any concern about themselves in their mind. All they care about is to help that one person.
However, if you think about it, there may be something in your subconscious. Maybe they're subconsciously thinking about a reward, or as my friend Jerry said it, that they can't bear to see that person dying.
But then again, some people's subconscious may be pure. And if you think about it again, can you control your subconscious thoughts? No. So does it count? Maybe.
It really depends on how you see it, and what you define as "truly selfless"
But I've read a book once and it had something in it, a message that I didn't remember word for word, so I'm just going to say the main point:
"If good things were done only when people were truly selfless, then there will be next to no good things in the world."
I might have worded that wrong, but here's an example the book gave:
Someone builds a hospital, but only so his name could be on the hospital's. Yes, it's selfish, but think about the benefits. Hundreds, maybe even thousands of people could be helped by the building of that one hospital.
So if we have to wait for ourselves to be truly selfless before helping others, will we ever do a good deed to others?