Don't duplicate content type header in local mode

[jamesls]

Fixes #310

[codecov-io]

Codecov Report

Merging #314 into master will increase coverage by <.01%.
The diff coverage is 100%.

@@            Coverage Diff             @@
##           master     #314      +/-   ##
==========================================
+ Coverage   87.32%   87.33%   +<.01%     
==========================================
  Files          19       19              
  Lines        1815     1816       +1     
  Branches      211      211              
==========================================
+ Hits         1585     1586       +1     
  Misses        178      178              
  Partials       52       52

Impacted Files	Coverage Δ
chalice/local.py	94.28% <100%> (+0.05%)	⬆️

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