This sounds like Hell's Gate by David Weber and Linda Evans, even though it's from 2006. From Wikipedia:
Sharona and Arcana are worlds in the multiverse which hold human civilizations. Both have discovered portals, which allow one to pass from one Earth to another, parallel Earth, which is almost always similar but uninhabited by sentient beings. Chains of universes linked by portals are called transit chains. Most universes have just one portal, or two; a few have three, and both civilizations have only found one with four.
And here's how the story begins with a bit more info than you can gleam from the jacket:
[...]The story begins with a Sharonan company's survey crew exploring a new universe, which they discover contains eight portals in close proximity. One of the members of the crew goes to hunt by himself, and has a surprise encounter with an Arcanan, also from a survey crew exploring the universe (although his crew is part of a governmental military organization). Each one is afraid that the other will shoot, so they raise their weapons, and then one panics and fires (who fired first was never made clear). The Sharonian managed to stagger back to his crew and warn them before expiring; they immediately began to move back toward the portal they had come from.
Right now, there's only a one more novel in the series – Hell Hath No Fury – but there might be a third book incoming in 2016.
Here's the cover for your viewing pleasure:
