Because the chemical in this case is something we have all the necessary things to produce.

I can't make energy (ie. food) from no input, but with some energy expenditure, my body could carry out the set of reactions to convert glucose (which is readily available in the diet) to Vitamin C.

Nearly every other mammal on the planet can make their own vitamin C. Aren't primates & guinea pigs the only exceptions?

Quoting http://en.wikipedia.org/wiki/Vitamin_C :

It is made internally by almost all organisms although notable mammalian group exceptions are most or all of the order chiroptera (bats), guinea pigs, capybaras, and one of the two major primate suborders, the Anthropoidea (Haplorrhini) (tarsiers, monkeys and apes, including human beings).

So not all primates.

Ok, look back at the wiki.

Do you know <i>why</i> you can't internally produce Vit C?

Because a mutation turned off our precursor's ability to do so, and (due to the abundance of vitamin C in their diet), wasn't immediately deleterous but instead managed to spread throughout the entire population.

Is the process to convert glucose into Vitamin C understood? Would it require something that could be seen as a tradeoff in our case?

Probably not a tradeoff. Scurvy is devastating and Wikipedia says an animal like a 70 kg goat makes ~13 grams of Vitamin C a day (which isn't very much of anything).

Scurvy might be devastating, but it's ridiculously easy to prevent. Especially nowadays.

Sure. I was responding to the tradeoff question. It just doesn't seem very likely that some animal survived because it wasn't making Vitamin C (the other case is some animal surviving even though it didn't properly make it).

I would assume so, just because I've never seen a shark eating a lime.

This doesn't mean that they don't tend secret lime farms on the ocean floor.

What kind of cellular machinery would be required? Where would this cellular machinery exist? Would we have a vitamin-C creating gland? How susceptible would this gland be to outright failure a la diabetes? The body could do a lot of things, but without a working alternative model simply saying the existing model is faulty suggests a deep understanding we clearly lack.

We already have the mechanism built into us. Other creatures do it. It's just broken in humans and our near relatives.