CSS3 selector first-of-type with class name

Question

Is it possible to choose the first element with a specific class name using the CSS3 selector:first-of-type? I've had no luck with my test, so I'm assuming it's not.

p:first-of-type {color:blue}
p.myclass1:first-of-type {color:red}
.myclass2:first-of-type {color:green}

<div>
  <div>This text should appear as normal</div>
  <p>This text should be blue.</p>
  <p class="myclass1">This text should appear red.</p>
  <p class="myclass2">This text should appear green.</p>
</div>