Chomp Snipes? You must be thinking of Garchomp C Lv. X with Dragon Rush, I'm talking about the Regular Garchomp from Supreme Victors which has a Poke-Body "Dragon Intimidation" that bounces Opponent's energies back to their hand whenever Garchomp is dealt damage or is Knocked Out.
The way Garchomp and Pidgeot benefit eachother is that Pidgeot increases the defending Pokemon's attack cost by {C}{C} with Headwind making it harder for them to land an attack and If they do manage to land an attack on the Active they return an energy back to their hand If Garchomp is dealt damage, thus potentially taking advantage of Speed Impact.
Nidoqueen RR, Blissey PT, or Ampharos Prime seem to work better with Pidgeot than Garchomp possibly. Or just heal Garchomp with Blissey to ensure that your Opponent's Active Pokemon has less energies to attack with.