I want to find out the name and issue number of a golden or silver age
horror comic book with the image of the Grim Reaper standing on a
chessboard on the cover.

The Grand Comics Database Project has an advanced search form where
one can search for a large number of elements, including text in a
Story Title, or Characters Appearing.

Searches for stories with "reaper" or "chess" in the title turned up
some titles, none of which seemed to be the one you were looking for.
But not all comics in the database have a scanned-in picture of the
cover, so it's not entirely clear that this lead is a dead-end.

I mention this in the hope that someone can put the resource to use in
their own attempt to answer this.

nauster-ga

I browsed through the scanned covers they have of Haunt of Fear, Tales
from the Crypt, and the Crypt of Horror and didn't see a match
(although they don't have all the covers for those titles).  They also
don't have covers any covers for The Vault of Horror.  Beyond those
titles I'm not too up on my older horror comics.

Grand Comics Database Project
http://www.comics.org/

Here are a couple of possibilities. These Golden Age comics contain
stories with titles that sound appropriate, but I have not been able
to find images of the cover art:

Star-Spangled Comics #125, "Murder on the Chessboard" (1952)

All-American Comics #90, "The Haunted Chessboard" (1947)

The cover of All-American Comics #90 can be viewed at::
http://www.comics.org/details.lasso?ID=6173

That place has lots of covers of Star-Spangled Comics, but unfortunately not #125.

You could try AC comics ( www.accomics.com ). They reprint a lot of
Golden Age comics, including old horror titles, westerns and science
fiction releases.

techtor

The answer is Eerie Adventures # 1.  It was published in the winter of
1951 by the Ziff-Davis Publ. Co.