diff --git a/xarray/core/accessor_interval.py b/xarray/core/accessor_interval.py
new file mode 100644
index 00000000000..cba6fa797e9
--- /dev/null
+++ b/xarray/core/accessor_interval.py
@@ -0,0 +1,100 @@
+from typing import Literal
+
+import numpy as np
+import pandas as pd
+
+from xarray.core.dataset import Dataset
+from xarray.core.extensions import (
+    register_dataset_accessor,
+)
+
+
+@register_dataset_accessor("interval")
+class DatasetIntervalAccessor:
+    def __init__(self, obj):
+        self._obj = obj
+
+    def decode_bounds(
+        self, name, *, closed: Literal["left", "right", "both", "neither"] | None = None
+    ) -> Dataset:
+        """Add a pandas IntervalIndex for indexing along a dimension.
+
+        This function uses the CF conventions on "bounds" variables to detect
+        the appropriate intervals to use. The ``"bounds"`` attribute on variable
+        ``name`` should link to a second variable that must be present. This 'bounds'
+        variable must be 2-dimensional with one of the dimensions being ``name``. The name
+        of the other dimension does not matter, but it must be of size 2.
+        A pandas IntervalIndex is created for the intervals defined by the bounds variable.
+
+        Parameters
+        ----------
+        name: Hashable
+            Name of the dimension coordinate for which an IntervalIndex is desired.
+        closed: {"left", "right", "both", "neither"}, optional
+            Which edge of the interval is closed. Must be specified if the ``closed``
+            attribute is not present. Note that the CF conventions do not dictate
+            how ``closed`` must be recorded. Usage of an attribute named ``'closed'``
+            is an Xarray-specific convention.
+
+        Returns
+        -------
+        Dataset
+        """
+        if not (bname := self._obj[name].attrs.get("bounds", None)):
+            raise ValueError(f"Attribute named 'bounds' not found on variable {name!r}")
+
+        boundsvar = self._obj[bname]
+        assert boundsvar.ndim == 2
+        (bdim,) = [dim for dim in boundsvar.dims if dim != name]
+        closed = closed or boundsvar.attrs.pop("closed")
+        assert self._obj.sizes[bdim] == 2
+        # TODO: error for cftime
+        index = pd.IntervalIndex.from_arrays(
+            boundsvar.isel({bdim: 0}), boundsvar.isel({bdim: 1}), closed=closed
+        )
+        return self._obj.drop_vars([name, boundsvar.name]).assign_coords(
+            {name: (name, index, boundsvar.attrs)}
+        )
+
+    def encode_bounds(
+        self,
+        name: str,
+        *,
+        suffix="bounds",
+        which: Literal["left", "mid", "right"] = "mid",
+    ) -> Dataset:
+        """Encode an IntervalIndex using the CF conventions.
+
+        Intervals are recorded using two variables:
+        - a 1D variable named ``'name'`` containing the "central value" (chosen by ``which``), and
+        - a 2D 'bounds' variable named ``'{name}_bounds'`` variable containing the left and right values
+          of the intervals stacked along a new dimension named ``'bounds'``.
+
+        For convenience, a new `PandasIndex` for the central values is assigned for the
+        dimension coordinate ``name``.
+
+        Parameters
+        ----------
+        name: Hashable
+            Name of the dimension coordinate for which an IntervalIndex is desired.
+        suffix: str
+            Suffix for the newly created bounds variable.
+        closed: {"left", "right", "both", "neither"}
+            Which edge of the interval is closed. The CF conventions do not dictate
+            how ``closed`` must be recorded, so the user is expected to provide it.
+
+        Returns
+        -------
+        Dataset
+        """
+        intarray = self._obj[name].data
+        bname = f"{name}_{suffix}"
+        bvar = xr.DataArray(
+            name=bname,
+            dims=(name, "bounds"),
+            data=np.stack([intarray.left, intarray.right], axis=-1),
+        )
+        bvar.attrs["closed"] = intarray.closed
+        newvar = self._obj[name].copy(data=getattr(self._obj[name].data, which))
+        newvar.attrs["bounds"] = bname
+        return self._obj.drop_vars(name).assign_coords({name: newvar, bname: bvar})