Is pyrex safe to use on a gas burner?

Where do you live? European Pyrex is made from borosilicate glass, the same as in laboratory's equipment; American Pyrex is made from common soda-lime glass.

If you are in America, don't bother trying it at all; soda-lime glass is sensitive to thermal shock. Even though it's tempered for kitchenware, it is nowhere near good enough for the burner.
In Europe, you could take your chances if you have a bowl you don't mind risking. However, there is still a significant chance that it will break on the burner some day. While I think that they use the same raw material for both kitchen dishes and laboratory test tubes (which are obviously OK on a gas burner), kitchen stuff is much thicker. This makes it much more likely to break under thermal expansion.

If you decide to make the experiment with a borosilicate Pyrex, take care to warm it gradually, starting with a small flame, and don't pour cold ingredients into it. Proceed at your own risk. And ask yourself if you really have no pots better suited for the task.

Just tried it - answer is no. Wish i'd read this before it cracked because of the heat.

From the PyrexLove FAQ:

Is it all right to use my vintage Pyrex directly on the stove?

We’d like to just nip this one in the bud and say - NO. Some pieces actually say “Not for stovetop”, but we never put vintage pyrex bowls, casseroles or whatever directly on the stove, ever. You can try it, but we’d rather not risk it.

But we do get a lot of people who are asking about Flameware and related Coffee makers / pots. Flameware was indeed meant to go directly on the stove, and that includes the coffee makers. However, some of those came with “heat spreader” grids to help diffuse the direct flame or intense heat from an electric stove. Some modern Pyrex (Visions, etc.) is also meant to go directly on the stove. Again, use your best judgement, and never temperature-shock the Pyrex by putting it on something cold!

No. Tried it today melting some butter on a low heat and it exploded violently sending glass shards in a 1 metre radius. Suprised me as I remembered using Pyrex test tubes over a Bunsen burner in science class. Won't be trying that again. Epic fail!

No no no. I cooked a whole meal and had to throw it away because my casserole dish exploded!

I was heating hot pan drippings to make a gravy on my stove top and after 5 minutes on low-med flame it exploded and glass (chunks and very fine pieces) flew 2 rooms away! Thank god no no one was hurt.

I have personally successfully broken a Pyrex dish through heat shock so I'd answer this question with a, "be careful," or, "probably best not to."

In my case I was making marzipan for my Christmas cake. I used the dish on top of a second steel pot containing water to warm the egg on the gas stove. Then transfered from that hot location to a bath of cold water to try to quickly cool and set the marzipan. After a few seconds in the cool water I heard a crack sound. In lifting the the dish up, the rim separated cleanly from the lower half of the dish leaving me with a glass hula-hoop.