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1
Cook lobster in pot of boiling salted water until shell turns bright red and meat is opaque in center, about 8 minutes.
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2
Drain.
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3
Transfer lobster to large bowl; cool.
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4
Working over same bowl to catch juices, twist off claws.
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5
Cut off tail.
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6
Cut lobster meat from shells.
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7
Reserve shells; scrape out green tomalley and discard.
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8
Cut meat into 1/2-inch pieces; cover and chill.
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9
Bring milk, 2 cups stock, bay leaf, thyme, parsley, and lobster shells with any accumulated juices to simmer in heavy large saucepan.
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10
Cover; simmer 10 minutes.
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11
Strain into large bowl.
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12
Return strained liquid to pan.
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13
Add chestnuts; bring to boil.
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14
Reduce heat; simmer uncovered until tender, stirring occasionally, about 15 minutes.
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15
Working in batches, puree soup in blender.
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16
(Lobster and soup can be made 1 day ahead.
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17
Cover separately; chill.)
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18
Bring soup to simmer.
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19
Stir in Madeira.
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20
Thin with more stock, if necessary, and stir until heated through.
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21
Season with salt and pepper.
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22
Meanwhile, melt butter in small skillet over medium heat.
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23
Add lobster meat; saute 1 minute to heat through.
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24
Ladle soup into bowls.
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25
Top with lobster meat.
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26
Sprinkle with minced fresh chives and serve.
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27
Available at specialty foods stores and some supermarkets.
