Hi Jason,

You can try the below approach.

1) Download the ckeditor standard package from this url https://ckeditor.com/ckeditor-4/download/.
2)Go to Your Name –>Develop –> Static Resources and click ‘New.’ Upload the zip file and call it ‘CkEditor.’
3)Try the below code in your org.I have made use of my custom object api name and custom object field api name. You can change it according to your requirement.
 

<apex:page standardController="Job_Application__c" >
<apex:includescript value="{!URLFOR($Resource.CkEditor,'ckeditor/ckeditor.js')}" />
<script type="text/javascript">
function ReloadCKEditor() {
   for(name in CKEDITOR.instances)
   {
       delete CKEDITOR.instances[name];
   }
   CKEDITOR.replaceAll();
}
</script>

    <apex:form >
        <apex:pageBlock id="thePageBlock">
            <apex:actionRegion >
                <apex:pageBlockSection id="pbs1" title="Information" columns="2"> 
                    <apex:inputField value=" {!Job_Application__c.CheckboxTest__c}">// Here Job application is my custom object and Checbox test is the checkbox 
                        <apex:actionSupport event="onchange" reRender="thePageBlock"  oncomplete="ReloadCkEditor();"/>
                    </apex:inputField>
                     </apex:pageBlockSection>
            </apex:actionRegion>
                <apex:pageBlockSection title="Rich Text Box Section" id="Section" columns="2"  collapsible="false" rendered="{!Job_Application__c.CheckboxTest__c==true}"> 
                          <apex:inputTextarea value="{!Job_Application__c.Test_Richtext__c}"  styleClass="ckeditor" richText="false" />//This is the rich text box area which will be displayed when you check the checkbox
                              </apex:pageBlockSection>
        </apex:pageBlock>
    </apex:form>
</apex:page>

Below is the output:



Let me know if it solves your problem.

Cheeres,
Rabindranath