I have no idea if it does anything for chest colds, but for colds in general, I'm a fan of the Vietnamese soup known as "Pho."
It's an oxtail stock, I think, with varied and unusual meats (I get the one with beef flank and tripe), rice noodles, thai basil, lime, plum sauce, sprouts (I leave em out), jalapenos, and general yumminess.
Not only is it indescribably delicious, but if you put enough of the provided hot peppers in it, it can do wonders for sinus clearing.
Here's one that worked well for me the other month - ginger tea with lemon and garlic.
To make: in a saucepan, heat 2 cups of water to boiling. Throw in chopped fresh ginger root (about 1 inch worth), a clove or two of fresh garlic (chopped, can be coarse), and a half lemon (quartered).
Reduce heat; let simmer for 20+ minutes.
Strain into a big mug. Sweeten with a large dollop of honey. Huddle over it; breath the steam in and sip slowly.
I have a list of other home remedies I could add, some of which I was afraid to try myself. F'rinstance, the "eat one clove garlic every hour until better" remedy ... 
peace, and get well,
Humidity as much as possible. Even sipping hot water at the office will help. And hand sanitizer.
Oh, and that hot water? When you get home add a squeeze of lemon, a pinch of nutmeg, and a slosh of whiskey.
I did have someone once tell me that when she started feeling unwell, she took cloves of garlic like pills. She claimed she never got sick. Let me know if you actually try it...I haven't...
Just down a fifth of Jack Daniels. Quickly.
Then work on the root cause. Take in a bunch of space heaters, an electric blanket, or (best solution) a portable firepit.
The root cause is the vent. Close it or block it up. That's what we do. We're a pro-active office....
Chai tea or tea with lots of spices. Ginger and turmeric are both good. Milk to smooth things down, honey to sweeten it, and whiskey to make you feel a lot better about the whole thing.
If you get bored with chicken soup, egg drop soup works the same way.
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