Update:
Chain
You can now use the chain feature in packed mode as describe in Eugene's answer.
Guideline
You can use a horizontal guideline at 50% position and add bottom and top (8dp) constraints to edittext and button:
<android.support.constraint.ConstraintLayout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools"
android:layout_width="match_parent"
android:layout_height="match_parent"
android:paddingLeft="16dp"
android:paddingRight="16dp">
<android.support.design.widget.TextInputLayout
android:id="@+id/client_id_input_layout"
android:layout_width="0dp"
android:layout_height="wrap_content"
android:layout_marginBottom="8dp"
app:layout_constraintBottom_toTopOf="@+id/guideline"
android:layout_marginRight="8dp"
app:layout_constraintRight_toRightOf="parent"
android:layout_marginLeft="8dp"
app:layout_constraintLeft_toLeftOf="parent">
<android.support.design.widget.TextInputEditText
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:hint="@string/login_client_id"
android:inputType="textEmailAddress"/>
</android.support.design.widget.TextInputLayout>
<android.support.v7.widget.AppCompatButton
android:id="@+id/authenticate"
android:layout_width="0dp"
android:layout_height="wrap_content"
android:text="@string/login_auth"
app:layout_constraintTop_toTopOf="@+id/guideline"
android:layout_marginTop="8dp"
android:layout_marginRight="8dp"
app:layout_constraintRight_toRightOf="parent"
android:layout_marginLeft="8dp"
app:layout_constraintLeft_toLeftOf="parent"/>
<android.support.constraint.Guideline
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:id="@+id/guideline"
android:orientation="horizontal"
app:layout_constraintGuide_percent="0.5"/>
</android.support.constraint.ConstraintLayout>
