Chesnaught

Chesnaught is the Kalos Grass-type starter in Gen 6, with an interesting Grass/Fighting typing. While it definitely looks cool and can be nostalgic among players who enjoyed playing Pokemon X and Y, its introduction into Pokemon Go is quite late meta-wise, as at this point of the game numerous Pokemon with superior stats and movesets have already been introduced. That doesn't mean Chesnaught is completely useless, it just won't be the best at what it does. 

Best PvE Offensive Moveset

• Vine Whip is the best fast move available and takes advantage of STAB. 
• Low Kick isn't as impressive, but can be used if a Fighting-type attacker is needed. 
• Smack Down lacks STAB and has no offensive use. 
• Frenzy Plant* is the best charge move on offense.
• Energy Ball and Solar Beam are a step down.
• Superpower can be paired with Low Kick to fulfill a Fighting-type role. 
• Gyro Ball and Thunder Punch have no use. 

Best PvE Defensive Moveset

• Smack Down has a considerably higher base power, and also covers against half of Chesnaught's weaknesses. 
• Vine Whip and Low Kick are inferior on defense, but perform very similarly to each other in this situation.
• Thunder Punch is, by far, the best Charged Move for Chesnaught on Defense. It comes out quickly and frequently, and has coverage against its single biggest weakness: Fighting Types.
• Frenzy Plant* hits hard and has STAB, making it a solid defensive option.
• Superpower as a 2-bar move is a bit slow on defense, but at the very least it's better than other options. 
• Energy Ball and Gyro Ball are easy to dodge; the former gets STAB while the latter hurts Ice and Fairy attackers. 
• Solar Beam is terrible for defense. 

Vine Whip is generally recommended for its significantly faster energy generation, as well as benefiting from STAB. Smack Down gives up faster energy gains for strong Rock-type damage, though it doesn't get STAB. Low Kick is a poor move. 

Superpower is a very strong move in PvP, offering very high damage for its low energy cost, but is risky to use with its self-debuff. Frenzy Plant is an insanely powerful attack, offering consistent high STAB damage at a fairly low cost. Energy Ball is a far inferior move in comparison. Gyro Ball requires more energy, lacks STAB, and its coverage isn't as useful. Solar Beam demands the most amount of energy, making it undesirable to use. Thunder Punch can be used to strike certain Flying-type Pokemon more effectively than its other moves, but Chesnaught has a tough time sacrificing either Superpower or Frenzy Plant.