All answers provided thus far result in potentially dangerous behavior as it is quite possible you select a dummy value that is actually part of the dataset. This is increasingly likely as you create groups with many attributes. Simply put, the approach doesn't always generalize well.
A less hacky solve is to use pd.drop_duplicates() to create a unique index of value combinations each with their own ID, and then group on that id. It is more verbose but does get the job done:
def safe_groupby(df, group_cols, agg_dict):
    # set name of group col to unique value
    group_id = 'group_id'
    while group_id in df.columns:
        group_id += 'x'
    # get final order of columns
    agg_col_order = (group_cols + list(agg_dict.keys()))
    # create unique index of grouped values
    group_idx = df[group_cols].drop_duplicates()
    group_idx[group_id] = np.arange(group_idx.shape[0])
    # merge unique index on dataframe
    df = df.merge(group_idx, on=group_cols)
    # group dataframe on group id and aggregate values
    df_agg = df.groupby(group_id, as_index=True)\
               .agg(agg_dict)
    # merge grouped value index to results of aggregation
    df_agg = group_idx.set_index(group_id).join(df_agg)
    # rename index
    df_agg.index.name = None
    # return reordered columns
    return df_agg[agg_col_order]
Note that you can now simply do the following:
data_block = [np.tile([None, 'A'], 3),
              np.repeat(['B', 'C'], 3),
              [1] * (2 * 3)]
col_names = ['col_a', 'col_b', 'value']
test_df = pd.DataFrame(data_block, index=col_names).T
grouped_df = safe_groupby(test_df, ['col_a', 'col_b'],
                          OrderedDict([('value', 'sum')]))
This will return the successful result without having to worry about overwriting real data that is mistaken as a dummy value.