The problem here is that the length of your array is undefined, and this confuses VBA if the array is explicitly defined as a string. Variants, however, seem to be able to resize as needed (because they hog a bunch of memory, and people generally avoid them for a bunch of reasons).
The following code works just fine, but it's a bit manual compared to some of the other languages out there:
Dim SomeArray(3) As String
SomeArray(0) = "Zero"
SomeArray(1) = "One"
SomeArray(2) = "Two"
SomeArray(3) = "Three"