Hi Michelle, You will have to use a primer like kilz first before you paint.
Here's a great video for you.
Chalk paint or milk paint can also be used to makeover Ikea furniture!
You need to use a good primer on the dresser before you paint. Kilz or Zinnser primer will cover the darkness as a first step before applying the lighter color paint of your choice. It may still take two coats of the lighter color, but the primer will give it a good base to adhere to.
I totally agree that you'll need to use primer before any paint. Even chalk paint. Just make sure that it's a bonding primer. Like Kilz, Zinnser, Stix, or BIN Shellac Based Primer. The primer will also help with coverage.