import matplotlib.pyplot as plt
       from matplotlib import style
       import pandas as pd
        style.use('fivethirtyeight')
        df = pd.read_csv('~/python/43068.csv')
        df.set_index('Date', inplace = True)
        # It works to here 
        df['Value'].plot()
         plt.legend()
         plt.show()

A CSV is purely a comma, not a comma and space by default. You can make the splitter something else, but your data is just a comma. You have that clear in your data, but your column header has a ', ' (comma, space). Thus, the column header is not "Value" ... it is " Value."

Date, Value

should be

Date,Value

You can always get a clean look, by doing:

print(df.columns)

which gives you

Index([' Value'], dtype='object')

and it's a little easier to see little things like that in the code.