Since herringbone weave was discovered long before viking era I though vikings might have used it. We were agruing with a friend of mine, but I could not find any reliable evidence.
The short answer is yes, although I must admit that I haven't had the opportunity to examine many Viking Age textiles personally. The most recent two I can think of were a plain tabby (a cloth fragment mixed in with a late Iron-Age necklace excavated on Bornholm) and a diamond twill (actually used in the molding process for a brooch also from Bornholm). However, there are some good sources out there. I'd especially point you to:
There's also older work on the textiles from Birka as well as on Oseberg, although I believe these are both in German (including Geijer's original 1938 study). However, I've also found a few sites that do a decent job sifting though the older literature. There's only a few places were substantial fragments of textiles have survived and attracted decent scholarly interest, particularly Oseberg (a female ship burial), Birka, and Haithabu (both grave fields outside of trading towns). I'd point you to:
The Viking Age Compendium. This page is very incomplete, although the sources cited are solid.
Viking Embroidery Stitches and Motifs. A thoroughly researched paper with an annotated bibliography. It's by Carolyn Priest-Dorman, who clearly knows her stuff 1 2.
For what it's worth, I've also found evidence that herringbone was being used slightly earlier in Merovingian France, ca. 400-500. It was also being used during the Viking Age across the Baltic in Poland.
For examples of Viking Age textiles, you can surf the National Museums of Denmark, Norway 1 2, and Sweden (type in 'textile' > click 'Sök' > click the + by 'Bild' > click 'Med bilder' > click the + by 'Tid' > click 'vikingatid'; sorry there's no easier way to link). You might also be interested in the good work going on at the Center for Textile Research. Their page on Viking Age clothing seems to include a sample of herringbone at the very bottom.
Incidentally, I recently learned that Viking Age Scandinavians would sometimes make patterns of S- and Z-wound threads, so textiles would appear to have zigzag patterns from the weave and grid patterns from the thread, and of course the way the patterns were perceived would depend both upon the light source and the angle of the viewer. Pretty cool, huh?