You can begin Chapter 1 by speaking with one of the following NPCs:
The Royal Courier. Located in the Greenwood Forest, west of the Lavender Coast Warpstone and south-east of the Archer camp, the Royal Courier will ask you to defeat the hooligans that stole his bag. - Sal Monella. Located in Blackspore Swamp, Sal will simply ask you to head to visit the Queen. This quest may not be available to you depending on whether you've completed other quests from Sal before.
- Starshine. Located at the Pixie Nursery south-west of Wugachug, Starshine will also suggest you see the Queen. Like Sal, if you have not completed some of her quests, Starshine may not offer this quest to you.
- Sorin. Located in the crystal mines of Snowhill, Sorin will recommend that you visit the Queen - again, if you have completed some of his quests.
- Henry Farnum. Located at Farnum's Farm, south of Crossroads, you will also need to complete Henry's other quests before getting a recommendation.
Because all recommendations except the Courier's require getting other quests done, some of which are also member-only, it is recommended to visit the Royal Courier. His quest does require combat, but is a non-member quest and will take less time investment than getting the recommendation from the other NPCs listed.
Regardless of who you talk to, they will give you a recommendation to go see Queen Valerian, located in the Royal Palace of Sanctuary, where the actual quest series will begin.