There are a grand total of 165 Chum Eggs scattered across the game map. Of these, you need to collect 100 to complete the Building a Queendom quest and the Chum Expert achievement.

For the first 5, next 15, and every subsequent 20 Chum Eggs (up to 100), the Chum Queen will give you a Chum Queen Tear. Each of these will increase your Stamina gauge substantially.

No more tears will be given after you've collected 100 eggs; instead you will be awarded the Chum Mask, which can detect any nearby uncollected eggs. If you collect a further 37 eggs, you will be given the Chum Top. To complete the outfit, collect the remaining 23 eggs and you will be awarded the Chum Skirt.

Here is a map of all 165 Chum Eggs in the game

High quality version[ibb.co].

Most of them are located near Fast-Travel waypoints, and you should be able to find 100 of them by normally progressing through the game. Due to the scale of the in-game world, it is not feasible to display the map at a greater zoom level.

Tip: To check which eggs you're missing and the region they are in, go into your save file (C:\Users\USERNAME\AppData\LocalLow\Shedworks\Sable\SaveData\sable_data_XXXXXXXX) and look under "ChumsMonitor".

Many thanks to ricbigo for the original map, and for finding the vast majority of the eggs. Credit also goes to TomOakhill for the updated map.