Sydney's 10mm "Ultra" SMG

is used by the relic hunter Sydney.

Location
Sydney the relic hunter carries this weapon. It can be obtained by either killing her (Note: You will receive NO BAD KARMA), letting her die, or finishing the quest Stealing Independence and giving her the A Note from Little Moonbeam's Father.

It can also be found by abandoning the "Stealing Independence" quest after helping her defend the area you first find her in. Let her run on into the dangers, and go do something else for a few hours (if not a couple days). Then come back and finish the "Stealing Independence" quest. Sydney will no longer be involved in the quest.

Later on, Sydney can also be found in various places around the Wasteland (one person found her near Raven Rock).

Bugs/Exploits
There is a bug/exploit in all versions of Fallout 3 that allows you to receive multiple copies of her Ultra SMG in perfect condition (along with 50 rounds of 10mm ammo). To trigger the exploit, after receiving the gun once choose the following dialogue options:

"Since we're done now, why don't you tell me about yourself?" "Nice gun. I've never seen one like that." (she mentions her father and re-triggers the option to ask about him)

"That's all for now, I guess" (taking you back one step in the dialogue tree)

"So, whatever happened to your father?"

and finally, "Sydney, I found a note from your father. He didn't abandon you."

You should then receive the Ultra SMG and ammo again. The above steps can be repeated as many times as you want for a limitless supply of both guns and 10mm ammo.

Sometimes, if you already completed Stealing Independence and later on found the recording, you can still show her to get her unique gun. She tells you she's heading to Underworld. However, when you get there you'll find her ammo stash in the 9th Circle bar but she won't be there. Check the Anacostia station entrance almost directly north of the Rivet City entrance. Go into the tunnels and she'll still be there, JUST starting her journey. You can escort her if you like, the walk isn't that long at all.

YouTube Videos
Obtaining Sydney's 10mm "Ultra" SMG R4tyj7G8Lo8