diff --git a/src/memory/FrameAllocator.cc b/src/memory/FrameAllocator.cc
index a862e0a..278873d 100644
--- a/src/memory/FrameAllocator.cc
+++ b/src/memory/FrameAllocator.cc
@@ -47,6 +47,25 @@ FrameAllocator::initialize(const StartupInformation& startupInformation)
     reserveRange(startupInformation.kernelStart, startupInformation.kernelSize() + mBitmapSize);
 }
 
+void*
+FrameAllocator::allocate()
+{
+    // Find the first bitmap with a free slot, and the first free slot, and return it.
+    const u32 pagesPerBitmap = Bitmap::length;
+    for (usize i = 0; i < mNumberOfPages; i += pagesPerBitmap) {
+        auto bitmap = mBitmap[i];
+        if (!bitmap.isFull()) {
+            for (usize j = 0; j < pagesPerBitmap; j++) {
+                if (!bitmap.isSet(j)) {
+                    bitmap.set(j);
+                    return addressOfPage(i * pagesPerBitmap + j);
+                }
+            }
+        }
+    }
+    return nullptr;
+}
+
 void
 FrameAllocator::reserveRange(u32 start,
                              u32 length)
@@ -88,4 +107,11 @@ FrameAllocator::reserveRange(u32 start,
     }
 }
 
+inline void*
+FrameAllocator::addressOfPage(usize page)
+    const
+{
+    return reinterpret_cast<void*>(page * memory::pageSize);
+}
+
 } /* namespace kernel */
diff --git a/src/memory/FrameAllocator.hh b/src/memory/FrameAllocator.hh
index e6cd407..bd07cdc 100644
--- a/src/memory/FrameAllocator.hh
+++ b/src/memory/FrameAllocator.hh
@@ -21,6 +21,14 @@ struct FrameAllocator
 
     void initialize(const StartupInformation& startupInformation);
 
+    /**
+     * Allocate a page. Find a free page, mark it in use, and return its
+     * address.
+     *
+     * @return The base address of a free page, or 0 if no page could be allocated.
+     */
+    void* allocate();
+
 private:
     typedef kstd::Bitmap<u8> Bitmap;
 
@@ -33,6 +41,9 @@ private:
 
     /** Reserve a range of memory. */
     void reserveRange(u32 start, u32 length);
+
+    /** Return the physical memory address of `page`. */
+    void* addressOfPage(usize page) const;
 };
 
 } /* namespace  */