first is CourseID Numeric? it should be.

Details

Dim selectcourse As Long
selectcourse = Me.CourseLb.Value

DoCmd.OpenForm "CourseTransF"
Me.RecordSource = "SELECT * FROM TransQ WHERE CourseID = " & selectcoure
Copy

CourseID is short text.  The legacy data that I will be importing requires a string.

Double Double Quotes

Dim selectcourse As String
selectcourse = Me.CourseLb.Value

DoCmd.OpenForm "CourseTransF"
Me.RecordSource = "SELECT * FROM TransQ WHERE CourseID = """ & selectcoure & """"

Another thing is your doing
Dim selectcourse As String
selectcourse = Me.CourseLb.Value

Then & selectcoure (spelling), missing the s from the variable name

Thanks Adam, I caught that too.

Well the form now opens but the WHERE statement is not working.  The records are not being filtered according to the WHERE statement.  I have verified that the variable has the correct value with a message box.

Private Sub CourseLb_AfterUpdate()

Dim selectcourse As String
selectcourse = Me.CourseLb.Value
MsgBox selectcourse

DoCmd.OpenForm "CourseTransF"
Me.RecordSource = "SELECT * FROM TransQ WHERE CourseID = """ & selectcourse & """"

CourseLB is a List Box. Correct?
You may need to access the Column property.

Yes that is a list box.  I did verify that the variable is getting the value from the list box.  Column property?

You're first column will be (usually) the ID. The value you a referring to may be in the second column.
    CourseLb.Column(1)

If that is not the case, please share the Row Source of your List Box.

Just re-read your code.
You are setting the Record Source of the current Form, not the Form you are opening.

Try using one line of code:
    DoCmd.OpenForm "CourseTransF",,,"CourseID=""" & CourseLB & """"

DoCmd.OpenForm "CourseTransF",,,"CourseID=""" & CourseLB & """"

Kevin this worked!  I really don't understand why it worked though.

As Rick once said "the old saying 'I don't know why it is not working' and after it works 'I don't know why it is working'
Great call Kevin!   John