diff --git a/base/subarray.jl b/base/subarray.jl
index 3a0be7d82b981..5d01340711c69 100644
--- a/base/subarray.jl
+++ b/base/subarray.jl
@@ -543,3 +543,46 @@ end
 
 # XXX: this is considerably more unsafe than the other similarly named methods
 unsafe_wrap(::Type{Vector{UInt8}}, s::FastContiguousSubArray{UInt8,1,Vector{UInt8}}) = unsafe_wrap(Vector{UInt8}, pointer(s), size(s))
+
+const ContiguousBitView = SubArray{
+    Bool,
+    N,
+    <:BitArray,
+    <:Union{Tuple{Vararg{Real}}, Tuple{AbstractUnitRange, Vararg{Any}}},
+    true
+} where N
+
+# This function is placed here because bitarray.jl is run in bootstrap before SubArray
+# is defined.
+function _count(
+        ::typeof(identity),
+        v::ContiguousBitView,
+        ::Colon,
+        init::Integer
+    )
+    T = typeof(init)
+    pi = only(parentindices(v))
+    (fst, lst) = (Int(first(pi))::Int, Int(last(pi))::Int)
+    fst > lst && return init
+    chunks = parent(v).chunks
+
+    # Mask away the bits in the chunks not inside the view
+    mask_start = typemax(UInt64) << ((fst - 1) & 63)
+    mask_end = _msk_end(lst)
+
+    start_index = _div64(fst - 1) + 1
+    stop_index = _div64(lst - 1) + 1
+    # If the whole view is contained in one chunk, then mask it from both sides
+    if start_index == stop_index
+        in_chunk =  count_ones(@inbounds chunks[start_index] & mask_start & mask_end)
+        return (init + in_chunk) % T
+    end
+    # Else, mask first and last chunk individually, then add all whole chunks
+    # in a separate loop below.
+    n = init + count_ones(@inbounds chunks[start_index] & mask_start)
+    n += count_ones(@inbounds chunks[stop_index] & mask_end)
+    for i in (start_index + 1):(stop_index - 1)
+        n += count_ones(@inbounds chunks[i])
+    end
+    return n % T
+end
diff --git a/test/bitarray.jl b/test/bitarray.jl
index fd5c1421a256f..7e20dc4254bb4 100644
--- a/test/bitarray.jl
+++ b/test/bitarray.jl
@@ -1303,6 +1303,11 @@ timesofar("datamove")
 
     @test count(trues(2, 2), init=0x03) === 0x07
     @test count(trues(2, 2, 2), dims=2) == fill(2, 2, 1, 2)
+
+    m = bitrand(25, 25)
+    for idx in Any[0x03, 5, 21:42, 7:6, :, 10:407, 64:70, 65:127, 315:384, Base.OneTo(111)]
+        @test count(m[idx]) == count(view(m, idx))
+    end
 end
 
 timesofar("find")