If you're going to break the rules at Yellowstone National Park, 4:30 a.m. is a great time to do so. The guard stations are closed and the roads deserted save for some shaggy bison and early-rising wildlife watchers. So it was in the wee hours of a July morning that a red Toyota van passed unnoticed beneath the Yellowstone Arch in Gardiner, Mont. The van carried three young men and their 11-foot kayaks, on their way to paddle a remote stretch of whitewater on the Yellowstone River.

If all went as planned, they would slip quietly out of the park's northern entrance a couple of days later without ever being seen by Park Service rangers.

For a while, things went smoothly, and Doug Ammons, Rob Lesser and Bob McDougall splashed their way down the churning world-class whitewater of Yellowstone's Grand Canyon. They camped, ate and got back in their boats to tackle the more challenging Black Canyon downstream. Then, as they scouted a class V rapid near the mouth of Hellroaring Creek, the distinct whup of helicopter blades emerged from the din of the crashing rapid. Glancing up, the trio saw men in Park Service uniforms glaring down.

"They looked like if they had machine guns they'd be shooting at us," says Ammons, who later wrote about the trip in his classic kayaking essay, "Counting Coup on the Yellowstone River."

Lesser – a former Yellowstone Park naturalist and Idaho-bred kayaking pioneer – had been arrested here before, forced to shoulder his loaded kayak and hike out of the canyon. Same river, same rapid. "Fuck off," Lesser remembers thinking. "I didn't want to be disrespectful, but I sure as hell wasn't carrying my boat out from there again."

The three jumped into their boats and the chase was on. At times, the helicopter flew deep within the canyon's walls, just 30 feet above the kayakers, whipping up a windstorm that threatened to tear the paddles from their hands. Commands blared from a megaphone. At one point, Ammons put his hand to his ear in a cheeky "I can't hear you" gesture and was blown over. He rolled upright and kept paddling.

In the end, though, there was no escape. The rangers arrested the men and locked their boats behind bars for two years. The kayakers got off with minor fines.

That was in 1986. Today, the high-stakes game of cat-and-mouse continues, because despite years of opposition from boating activists and kayaking's evolution into a mainstream activity, it remains a federal offense to kayak, raft or otherwise float any whitewater in Yellowstone National Park.

"Yellowstone has the largest block of rivers in the country that is prohibited to paddling," says Kevin Colburn, stewardship director for the paddling group American Whitewater.  "It's an anomaly in the entire national park system."

Now, paddlers hope a new river management plan for two designated wild and scenic rivers elsewhere in the park will provide the opening they need to spur a new discussion about Yellowstone's waters. But they face an upstream paddle. A decades-long battle over the issue has divided the conservation community, and the Park Service says Yellowstone's resources are already stretched thin. Kayakers aren't the only group clamoring for access. Stand-up paddleboarders, snow kiters, snow bikers and BASE jumpers – along with ATV riders, remote-control airplane enthusiasts and Segway operators – have all requested access to Yellowstone's iconic landscapes. Which raises a sticky question for national parks all over the country: Where do you draw the line?