Getting Gnome Past the Farmhouse Helicopter, without cheats

• The helicopter is more interested in the car than in you
  
• Once the car passes through the tunnel, the helicopter will never revisit the area before the tunnel
  
• When the car passes through the tunnel, the helicopter moves off to a distance and will not attack again until you reach it
  
• Once you reach it, if you proceed past it on foot it will eventually return to fire upon the car - use the nearby train for cover until it losses interest in you
  
• Don't get too far away from Alyx, otherwise you'll get a mission failure and reload last save
  
• Alyx cannot be killed by the helicopter, and the car cannot be damaged
  
• Use these facts to move Gnome through the area on foot, untouched by the helicopter

So that we're all on the same page, I'll begin by describing the chase sequence, taking note of various landmarks along the way and breaking the chase into three sections based on the behavior of the helicopter.

Section One begins after you fail to kill the Combine Advisor and are subsequently attacked by Combine soldiers and a single Hunter. Upon escaping in your car, a Combine Helicopter pursues. The chase leads from the farmhouse straight ahead past a couple regular zombies and through a windbreak where you'll make a hard left turn onto train tracks. Follow the tracks to a long tunnel that leads to an area transition.

Section Two begins following the area transition. In this section you'll exit the tunnel, jump over a ramp into a sign (yeehaw!), and be ambushed from above by a Fast Zombie that Alyx kicks from the car as you make a hard 180 degree turn onto an adjacent set of railroad tracks. Section Two ends below several bridges home to barnacles and a Zombine camp - beyond the last bridge, Section Three and the helicopter await.

Section Three features another open-air chase characterized by two gentle left turns separated by a second ramp jump, various other obstacles, and constant bombardment and gunfire before arriving at the Resistance Base where your car breaks down and you destroy the helicopter using its own bombs against it.

Here's an alternate view of Sections Two and Three:

The easiest and safest way to get Gnome through this section is to leave him at the Farmhouse!

When you first arrive at the location, find a safe place to hide Gnome where he won't get blasted or kicked and subsequently lost when you get ambushed, then, when you do get ambushed, leave him behind and drive like hell to the tunnel.

Here's the trick: once the car passes through the area transition within the tunnel, the helicopter assumes a new position on the far side of the tunnel and waits for you there. This means you can go back to the Farmhouse to retrieve Gnome without fear of aerial assault.

To get Gnome through this section, leave Alyx and the car just inside the tunnel (after passing back through the area transition) and continue forward (with Gnome) on foot. You will NOT be ambushed by the Fast Zombie from above - that's a scripted event tied to the car, not to Gordon - and you will NOT be attacked by the helicopter.

Walk past the jump ramp, under the bridges, through the 180 degree turn, through the Zombine/Barnacle camp, back under the bridges, then STOP - this is the end of Section Two. The helicopter hovers just beyond the final bridge, but will not attack provided you stay under cover (also, if you continue forward you'll meet with mission failure for leaving Alyx behind).

The image below shows the scene in front of you as you stand under the bridge at the end of Section Two. To your right is a small alcove perfect for parking the car prior to Section Three, and before you is a partially derailed train along the far retention wall. Throw Gnome towards the nearest train car then walk back to the tunnel.

Drive through Section 2 and park the car in the spot shown in the image above. Run forward and crouch underneath the nearest train car to hide from the helicopter. Recover Gnome with the Gravity Gun, then exit the far side of the train car such that you are between the train and the retention wall. Toss Gnome forward and play a short game of run and hide with the helicopter, which quickly loses interest in you and moves back to fire upon the car.

Don't worry, Alyx will be fine.

With the helicopter otherwise preoccupied, enjoy a quite, undisturbed stroll to the Resistance Base, chuck Gnome over the gate, then return to Alyx. Floor it to the base and you're done!