The Club at Stablechase, Houston, TX, 77070. Bedrooms: 1-3. The Club at Stablechase was created for those who know what they want out of life! Our elegant homes of distinction provide carefree living with personalized service. You'll be surrounded by natural beauty and vitality. With our central location, you are just minutes from fine dining, shopping and recreation. With features such as a clubhouse and a fitness center, you'll be living the good life at The Club at Stablechase.