Use the original df1 indexes to create the series:

df1['e'] = pd.Series(np.random.randn(sLength), index=df1.index)

Edit 2015
Some reported getting the SettingWithCopyWarning with this code.
However, the code still runs perfectly with the current pandas version 0.16.1.

>>> sLength = len(df1['a'])
>>> df1
          a         b         c         d
6 -0.269221 -0.026476  0.997517  1.294385
8  0.917438  0.847941  0.034235 -0.448948

>>> df1['e'] = pd.Series(np.random.randn(sLength), index=df1.index)
>>> df1
          a         b         c         d         e
6 -0.269221 -0.026476  0.997517  1.294385  1.757167
8  0.917438  0.847941  0.034235 -0.448948  2.228131

>>> p.version.short_version
'0.16.1'

The SettingWithCopyWarning aims to inform of a possibly invalid assignment on a copy of the Dataframe. It doesn't necessarily say you did it wrong (it can trigger false positives) but from 0.13.0 it let you know there are more adequate methods for the same purpose. Then, if you get the warning, just follow its advise: Try using .loc[rowindex,colindexer] = value instead

>>> df1.loc[:,'f'] = pd.Series(np.random.randn(sLength), index=df1.index)
>>> df1
          a         b         c         d         e         f
6 -0.269221 -0.026476  0.997517  1.294385  1.757167 -0.050927
8  0.917438  0.847941  0.034235 -0.448948  2.228131  0.006109
>>>

In fact, this is currently the more efficient method as described in pandas docs


Edit 2017

As indicated in the comments and by @Alexander, currently the best method to add the values of a Series as a new column of a DataFrame could be using assign:

df1 = df1.assign(e=pd.Series(np.random.randn(sLength)).values)