diff --git a/01_introduction_to_algorithms/elixir/01_binary_search.exs b/01_introduction_to_algorithms/elixir/01_binary_search.exs
new file mode 100644
index 0000000..0569dcc
--- /dev/null
+++ b/01_introduction_to_algorithms/elixir/01_binary_search.exs
@@ -0,0 +1,29 @@
+defmodule BinarySearch do
+  def search(list, item) do
+    low = 0
+    high = length(list) - 1
+
+    do_search(list, item, low, high)
+  end
+
+  defp do_search(_, _, low, high) when high < low, do: nil
+
+  defp do_search(list, item, low, high) do
+    mid = div(low + high, 2)
+    guess = Enum.at(list, mid)
+
+    cond do
+      guess == item -> mid
+      guess > item -> do_search(list, item, low, mid - 1)
+      true -> do_search(list, item, mid + 1, high)
+    end
+  end
+end
+
+my_list = [1, 3, 5, 7, 9]
+
+IO.puts(BinarySearch.search(my_list, 3))
+# => 1
+
+IO.inspect(BinarySearch.search(my_list, -1))
+# => nil