I have had this problem for a long time. I have used duckduckgo.com and this website to try to find a solution, to no avail.

Current version of chromium is: 57.0.2987.98-1~deb8u1
But like I have said, it has been a constant PITA for quite a while.

The tab that appears when chromium is started is labeled:
"file:///usr/lib/chromium/chromium
Which always appears in my download directory, even when I change the download directory"

When I "hit" it with file, it says that it is:
"ELF 64-bit LSB shared object, x86-64, version 1 (SYSV), dynamically linked, interpreter /lib64/ld-linux-x86-64.so.2, for GNU/Linux 2.6.32, BuildID[sha1]=e206e3acde7124fca936e2a5b2fed8196cc5fb46, stripped"

It *always* appears when I start chromium it is named "chromium" in my download directory, and if the file exists, it is called "chromium (1)", and so forth.

I am running Debian version 8.8 right now.

OK, does anyone have any idea why I get this damnable file in my download directory, and how can I get this file to stop appearing when I start chromium?

That you for your time, and have a good day.

Check your settings for ...Setings (click on the three vertical dots near the upper right, and select Settings).

Scroll down to "On Startup". It is either set to start on your Home Page (which is set to file:///usr/lib/chromium/chromium) or it is set to Open a specific page/set of pages, which includes file:///usr/lib/chromium/chromium.

Another possibility is that the launcher you are using to start Chromium is messed up in some weird way so that it is doing something like running "chromium chromium" or something like that. What method are you using to start Chromium?

Did: 1: Open new page tab,
2: Continue where you left off,
3: Open a specific set of pages.

BUT

I executed it via a command shell, and it worked fine, no extraneous file in Download directory.

I tried to edit "Edit Applications" and had it "run in terminal" but the file showed up when it started.

I start chromium via a launcher on my panel, but when I use the menu, that file doesn't appear. So I guess that the launcher on my panel is bugged.

OK, this is probably acceptable.
However, what is wrong with the launcher on my panel???

Thank you for your suggestions that had me, sort of, come to a solution.

I guess I will call this "[SOLVED]"

What desktop environment are you using? I know with XFCE4 you can right click on a panel launcher to edit its properties. And switching whether or not it does "run in terminal" in XFCE4 will have no effect on what it actually does (other than whether or not it provides a terminal for console feedback). The simplest thing in XFCE4 would be to simply remove the offending Chromium launcher and then add a new one. XFCE4 in Debian 8 is slightly less advanced in this regard than in Debian 9, but it works just fine for this stuff.

I use KDE4