The object was part of a pair of plastic sunglasses (the stick that
goes around the ear at one end, and connects to the rim of the lens at
the other.) It had broken off the glasses, and was lying on top of the
dryer, when it accidentally fell into the hole on top of the dryer
where the lint trap goes into, when I had removed the trap to clean the
lint off it one day. The opening of this hole is too narrow for me to
reach in with my hand to try and retrieve this object, and I also tried
checking at the other end, where the duct connects to the back of the
dryer, but I couldn't get at it from there either.

So basically, I'm afraid that this object remaining where it is (stuck
in there somewhere), might be a potential fire hazard, because of the
high temperatures that are reached there (I noticed that this area is
all metal, suggesting that plastic might not be safe there.) I called
an appliance repair person, and what he said was that as long as we're
not hearing any noise (like the object rattling around) when we start
the dryer, then it should be fine. I don't understand the logic behind
this, and this guy had a pretty thick Russian accent so I could barely
comprehend him, so anyway I just thought I'd toss this problem out to
this newsgroup for second opinions on the matter (and to be on the safe
side.) Thanks!!

Since you seem to be able to see the glasses, you can operate the dryer
carefully and check to see whether they are melting. If they did melt
it would provide fuel for a fire. Dryer fires are more common than
people think. Usually, the fire comes from lint buildup in the dryer
vent and can be initiated by light clothes being pulled in past the
drum seals due to improper maintenance of the drum slides/rollers.

I would use one of those flexible tools with three expanding fingers to
retrieve the glasses. These tools are available at the hardware store
or auto parts store. They cost under $2 where I live. You should have
one of these tools around the house anyway.

Check out this web site. http://www.applianceaid.com/
You may be able to disasemble and clean out the lint trap area.

Clark and Al- thank you both so much for your replies!

So first, Al: actually, I was not able to see the object (I guess I
should have explicitly stated that in my original post, sorry for the
confusion.) But I do definitely agree with you about dryer fires,
which was why I was as concerned about this as I was.

And Clark: I poked around that site, and lo and behold...

http://www.applianceaid.com/fanblower.html

So I guess I'm not the first person that this has happened to!
Well, I had the husband remove that back panel of the dryer according
to the instructions on that page, and- voila! Not only was he able to
retrieve that object that was from the sunglasses, but he also got out
from there a small pencil, a paper clip, a toothpick, a bobby pin, and
a whole, whole lot of dirt and lint!!

So thanks so much guys, I am so very grateful that this problem is now
taken care of (it's a load off my mind, and I now know how to deal with
this sort of thing in the future, and I now have a great online
resource to consult in the event of any other appliance-related problem
that may come up in the future!) Thanks again.