Did you set the server to unpure?
sv_pure 0

I dunno how q3 loads files but you could also try to rename the .pk3 with a name that loads later than pak0.
zzz_sprites.pk3 for example

sv_pure 0, and zzz_chat.pk3. Doesn't work :(

Did you try replacing the .tga file in pak0? I assume your using this only for movie purposes and not for playing :)
(I recommend making a backup for pak0 first)

I didn't do that yet, but it may be possible. Trying it right now, thanks dude!

http://kepfeltoltes.hu/110213/shot0006_www.kepfeltoltes.hu_.jpg

It puts it in upside down, with a black background, wtf :(

I dunno why it's upside down but the black background is because you probably didn't save it with an alpha channel.
Make sure you edit the .tga with an editor that supports alpha channels, like Photoshop

http://www.mikemartin1200.com/defrag/q3_glowy_chat_balloon.zip

:]

Saw that, but it still doesn't work even if I replace the .tga file. :(

upload the pk3 somewhere

Are you saving the .TGA as 24 bit?
You'll need the extra 8 bits for Alpha so make sure you save it as 32 bit.

Also in the game try setting... (prolly not req's but hey)

r_colorbits 32
r_depthbits 32

And ensuring the image size are the SAME dimensions as the default.

I have no clue if the above works, but seems like a technical prerequiste to me.

As for it being wrong way around try flipping the image in photoshop and resaving.

32 bit. And it looks alright in PS. It doesn't however in game (flipped).

olol :(

Delete the balloon4.tga file from pk0/sprites.
Save the attached file into that dir and don't touch filename etc.
http://www.megaupload.com/?d=UIVFBZB2

Thanks :)