I'm updating details on this hike two years after-the-fact but I happened to visit the same area recently while doing other close by mountains. The hike to Chupadera Mountains actually begins on the Bosque Del Apache Wildlife Refuge from NM-1 where there's a parking area and trailhead. An unofficial trailhead starts off Interstate 25 at virtual mile marker 132.8 but for obvious reasons that starting point is not encouraged and shouldn't be used for groups. Should you elect to start from I-25, the trail can be access from either side of the interstate as the trail passes under the interstate although the southbound side is best as you can park completely off the highway behind a guard rail. It's also easy to spot, as the guardrail is clearly visible as you pass mile marker 133. The trail is marked and well-worn. I started the hike from I-25.