What size is the chest on the Adventuring Gear table? Is it considered medium, large, or something else?

12 cubic feet of space

so something like 2 ft x 3 ft x 2 ft

3 feet being the longest dimension I would put it as small to medium sized

Mmm...think the average chest size is a solid B-cup, really.

But yes.  Probably Small, if and when it matters.  On the chunkier side of Small, but if your average halfling has to bend to fit in a chest, then Small is the way to go.

This is exactly what I thought it would be.

Now if you had been talking about this book, (Morningwood Everybody Loves Large-Chests ) then I would be surprised.

12 cubic feet is close to 8 cubic feet than 27, so it is a bit larger than 2x2x2 (less than small), not as big as 3x3x3, and no where near as large as 5x5x5 (Medium)

So a normal sized chest is definitely a Small sized object.

If small is 3x2x2 and medium is 5x5x5, what size are large and bigger (huge?) chests?

. . . for that matter, what size would a tiny chest be?

A tiny chest fits a standard set of polyhedral dice?

Quote from KaosKubes >>

If small is 3x2x2 and medium is 5x5x5, what size are large and bigger (huge?) chests?

. . . for that matter, what size would a tiny chest be?

 Large Sized objects of any kind are 10 x 10 x 10.

Huge sized objects of any kind are 15 x 15 x 15

Gargantuan are 20 x 20 x 20 or bigger.

I am not sure about Tiny sized objects,

Tiny is apparently 2.5 X 2.5. 

The Size section on 'Race' in the PHB cites that Small characters are "between two and four feet tall".  Would follow that Tiny is, thusly, below two feet in its longest dimension.  A rule of thumb I'd generally use as a DM is "can this be lifted/held/manipulated with one ordinary human hand?  Tiny.  Does this require two hands to pick up/hold/manipulate?  Small."

Objects don’t follow the same sizes as creatures do. A Longsword is considered a Small object, whIle a chair is considered Medium. I would say a chest is either Small or Medium, depending on its total length.

Quote from IamSposta >>

Objects don’t follow the same sizes as creatures do. A Longsword is considered a Small object, whIle a chair is considered Medium. I would say a chest is either Small or Medium, depending on its total length.

 The DMG lists a chest as an example of a small object. I don't remember ever seeing a size for a longsword or chair, but a flying sword's attack and traits suggest it's a longsword, and it's small.

Quote from ChoirOfFire >>

Quote from IamSposta >>

Objects don’t follow the same sizes as creatures do. A Longsword is considered a Small object, whIle a chair is considered Medium. I would say a chest is either Small or Medium, depending on its total length.

 The DMG lists a chest as an example of a small object. I don't remember ever seeing a size for a longsword or chair, but a flying sword's attack and traits suggest it's a longsword, and it's small.

 
Yeah, I remembered seeing a longsword listed as small somewhere, not sure where. Maybe in a spell effect or something? 🤷‍♂️ Somewhere at any rate. I’m not surprised that a chest is Small, it seems anything around that length is Small.

Note that many actual chests, depending on what they're expecting to store, will be Tiny, given that a 12 cubic foot chest can hold on the order of 500,000 gold coins (exact amount depends on how its stacked, 12 cubic feet of gold is actually more on the order of 700,000, but coins don't stack perfectly efficiently).

Quote from Mog_Dracov >>

Quote from KaosKubes >>

If small is 3x2x2 and medium is 5x5x5, what size are large and bigger (huge?) chests?

. . . for that matter, what size would a tiny chest be?

 Large Sized objects of any kind are 10 x 10 x 10.

Huge sized objects of any kind are 15 x 15 x 15

Gargantuan are 20 x 20 x 20 or bigger.

I am not sure about Tiny sized objects,

As was mentioned objects don’t follow creature size necessarily and even large creatures are not 10x10x10 but just control that much space. 

That said. You could probably consider:

large objects greater than 5x5x5

huge greater than 10x10x10 

gargantuan greater than 15x15x15

Or just ask your DM.