Absolutely spot on MrShorty sir, that solved my problem. For others that may find this, here is the subroutine that creates a chart from dynamic data as I have found that the order definitely does matter.
Sub History_Chart()
    Dim hData As Range
    Dim hChart As Shape
    
    Set hData = Range(BatchSearch.Offset(0, 1), BatchSearch.End(xlToRight)).Resize(5)
    With inspHist.ChartObjects.Add(Left:=100, Width:=375, Top:=75, Height:=225)
        With .Chart
            .ChartType = xlColumnClustered
            .SetSourceData Source:=hData
            .PlotBy = xlRows
            .Parent.Name = "Inspection_Chart"
        End With
    End With
    inspHist.Visible = xlSheetVisible
    inspHist.Select
End Sub

BatchSearch is a globally defined "Range" Variable declared at the beginning of the module.

Kind regards
Rob