Good afternoon:

I have a tree plant in my living room and it seems to be dying. I just noticed this morning that the soil is full of a centipede-type looking bug.

What can I do to save my tree and get rid of those things? Any assistance will be greatly appreciated.

Lolita

It's not clear if the pest are the cause of your trees problem or not, they feed on mico material in the soil and the smaller roots sometimes.
If you want them gone (who wouldn't) you can take the plant out of it's pot and stick the entire root-ball in water for 15 min to a half hour or so, like inside a pail or anything wide enough to take most of the root-ball.
All the pest should come floating to the top of the water for air, scoop them out and replace any lost soil. You might want to re-check the root-ball for damage and any stragglers.